Structural illumination and evanescent coupling for the extension of imaging interferometric microscopy

ABSTRACT

In accordance with the invention, there are imaging interferometric microscopes and methods for imaging interferometric microscopy using structural illumination and evanescent coupling for the extension of imaging interferometric microscopy. Furthermore, there are coherent anti-Stokes Raman (CARS) microscopes and methods for coherent anti-Stokes Raman (CARS) microscopy, wherein imaging interferometric microscopy techniques are applied to get material dependent spectroscopic information.

RELATED APPLICATIONS

This application claims priority from U.S. Provisional PatentApplication Ser. Nos. 61/017,985, filed Dec. 31, 2007; 61/089,669, filedAug. 18, 2008; and 61/115,246, filed Nov. 17, 2008, which are herebyincorporated by reference in their entirety.

GOVERNMENT RIGHTS

This invention was made with government support under Contract Nos.HR0011-1-0006 awarded by the Defense Advanced Research Projects Agencyand FA9550-06-1-0001 awarded by the Air Force Office of ScientificResearch. The government has certain rights in the invention.

FIELD OF THE INVENTION

This invention relates generally to microscopy, and, more particularly,to an imaging interferometric microscope; coherent anti-Stokes Raman(CARS) microscope; methods for applying the imaging interferometricmicroscopy to coherent anti-Stokes Raman (CARS) microscopy; methods tosimplify the approaches to imaging interferometric microscopy thatrequire less, or no, access to the optical path after the objective lensand so can be applied to existing microscopes; and for providing anoptical resolution up to about λ\4n, where n is the substrate refractiveindex and λ is an optical wavelength.

BACKGROUND OF THE INVENTION

Optical microscopy is among the oldest applications of optical scienceand remains one of the most widely used optical technologies. In spiteof impressive results obtained by fluorescent microscopy in exceedingthe classical diffraction limit, non-fluorescent transmission/reflectionmicroscopy remains an important field of modern research. However, usingtraditional illumination schemes, resolution is limited to ˜κ₁λ/NA whereλ is the source wavelength and NA is the numerical aperture (sine of thehalf-acceptance angle) of the imaging objective lens. The “constant” κ₁depends on both the details of the image and on the illumination scheme.Hence, traditional approaches to improve resolution are either to useshorter wavelengths and/or to use larger numerical-aperture lenses. Forbiological samples, however, the wavelength is constrained to thevisible spectral range because ultraviolet photons can damage samples.In many practical cases, even for inorganic samples, the wavelength islimited to the deep ultraviolet (for example 193 nm) since transmissiveoptical materials become difficult at shorter wavelengths (fused quartzhas a cutoff at ˜185 nm). Furthermore, a disadvantage of using a high-NAlens is the resulting short depth-of-field (an essential feature ofachieving high resolution in a single image; typically thedepth-of-field scales as κ₂λ/NA² where κ₂ is a second “constant” oforder unity). The depth-of-field decreases rapidly as the NA isincreased to increase the resolution. In addition, the field of view(the area over which the resolution is achieved) and the workingdistance (the distance from the final lens surface to the object plane)are reduced for higher-NA optical systems. These latter two issues canbe surmounted by more complex objective lenses, with an increase in thecost of manufacturing. These tradeoffs are well known and are discussedin many microscopy overviews.

Synthetic aperture approaches, such as, for example, imaginginterferometric microscopy (IIM) extend the collected spatialfrequencies to improve the image. IIM uses a low-NA objective and yetprovides a resolution approximately a factor of two better than thatavailable even with a high-NA objective using conventional coherent orincoherent illumination. A major advantage is that the depth-of-field,field-of-view and working distance associated with the low-NA system areretained, but the final composite image has a resolution at the linearsystem limit imposed by the transmission medium (≧λ/4 where λ is thewavelength in the transmission medium), and significantly better thanthat accessible with even a high NA lens using conventional (coherent orincoherent) illumination approaches. As is well-known, using off-axisillumination provides enhanced resolution over that available witheither of the standard illumination schemes discussed above, but thereis some distortion of the image associated with the resultantnon-constant transfer function for different regions of frequency space.This non-uniform frequency-space coverage can be addressed withappropriate pupil plane filters and by combining partial imagescorresponding to different parts of frequency space, as has beenpreviously demonstrated in the case of imaging interferometriclithography.

An exemplary IIM with two offset partial images, one each in orthogonalspatial directions can result in an increased resolution by three timesusing about 0.4-NA objective and 633-nm He—Ne laser. Furthermore, IIMrequires building an interferometric system around the objective lenswhich is an issue for wide-spread adoption of this approach, and inparticular towards its adoption to the existing microscopes. In theprior art, this interferometer required additional optics to relay thepupil plane of the collection objective to convenient location; this isstraightforward but required significant additional optics. Hence, thereis a need for a new approach that does not require a large change to theimaging optical system that comprises the objective lens and subsequentoptical components.

The prior art imaging interferometric microscopy was able to imagemaximum spatial frequency of 2π/λ e.g. to the linear system's limit ofthe air (transmission medium between the object and the lens). Theultimate linear system's limit is 2πn/λ, which reflects the use of animmersion medium of refractive index n. Even though materials withrefractive indices of upto about 3.3 are known at some opticalwavelengths, the highest numerical aperture available for the immersionmicroscopy is about 1.41 limited by the refractive index of the glassused to make the lens, by the refractive indices available for the indexmatching fluids, and the well known difficulties of making aberrationcorrected optics of high NA. Hence, there is a need for a new approachthat can achieve this linear system's limit without requiring high indexmatching fluids or high NA lenses.

SUMMARY OF THE INVENTION

In accordance with various embodiments, there is an apparatus formicroscopy including an object plane on which can be disposed a firstsurface of a substrate, wherein the substrate is characterized by ahomogeneous refractive index (n_(sub)) and a surface normal. Theapparatus can also include a first optical system disposed to provide asubstantially coherent illumination of the object plane, theillumination characterized by a wavelength λ and a radius of curvatureand disposed at one of a plurality of incident wave vectors from about 0to about 2π/λ with respect to a surface normal of the substrate and at aplurality of azimuth angles spanning 0 to 2π. The apparatus can furtherinclude a second optical system disposed to collect portions of theillumination scattered from the object plane, the second optical systemhaving an optical axis disposed at one of a plurality of center wavevectors from about 0 to about 2π/λ with respect to the substrate surfacenormal and at the azimuth angle corresponding to the illumination of thefirst optical system, wherein the second optical system is characterizedby a numerical aperture (NA). The apparatus can also include a thirdoptical system disposed between the optical path of the first opticalsystem and an entrance aperture of the first optical element of thesecond optical system to provide interferometric reintroduction of aportion of the coherent illumination (reference beam) into the secondoptical system, wherein each of an amplitude, a phase, a radius ofcurvature, and an angle of incidence of the reference beam is adjustedsuch that a corrected reference beam is present at the image plane ofthe second optical system. The apparatus can further include anelectronic image device disposed at an image plane of the second opticalsystem that responds linearly to the local optical intensity andtransfers the local optical intensity map across the image plane (asub-image) to a signal processor device in electronic form, a device foradjusting the first, the second, and the third optical systems tocollect sub-images for different pairs of the pluralities of incident(first optical system) and collection center (second optical system)wave vectors so as to sequentially obtain a plurality of sub-imagescorresponding to a plurality of regions of spatial frequency space, andan electronic device to sequentially receive the electronic form of thesub-images and manipulate the sub-images to correct for distortions andalterations introduced by the optical configuration, store, and combinethe plurality of sub-images corresponding to the plurality of regions ofspatial frequency space to create a composite image.

According to another embodiment, there is a method for microscopyincluding providing an object disposed over a planar substrate, whereinthe substrate is characterized by a homogeneous refractive index(n_(sub)) and a surface normal. The method can also include providing afirst optical system to illuminate the object with substantiallycoherent illumination, the illumination characterized by a wavelength λand a radius of curvature and disposed at one of a plurality of incidentwave vectors from about 0 to about 2π/λ with respect to a surface normalof the substrate and at a plurality of azimuth angles spanning fromabout 0 to about 2π. The method for microscopy can further includeproviding a second optical system disposed to collect portions of theillumination scattered from the object plane, the second optical systemhaving an optical axis disposed at one of a plurality of center wavevectors from about 0 to about 2π/λ with respect to the substrate surfacenormal and at the azimuth angle corresponding to the illumination of thefirst optical system, wherein the second optical system is characterizedby a numerical aperture (NA). The method for microscopy can also includeproviding a third optical system disposed between the optical path ofthe first optical system and an entrance aperture of the first opticalelement of the second optical system to provide interferometricreintroduction of a portion of the coherent illumination (referencebeam) into the second optical system, wherein each of an amplitude, aphase, a radius of curvature and an angle of incidence of the referenceis adjusted as required such that a corrected reference wave is presentat the image plane of the second optical system. The method formicroscopy can also include recording a sub-image of the object at anobject plane using an electronic image device, wherein the sub-image isformed as a result of interference between the scattering resulting fromthe coherent illumination of the object and the reference beam,adjusting the first, the second, and the third optical systems tosequentially collect a plurality of sub-images corresponding to aplurality of regions of spatial frequency space, manipulating each ofthe plurality of sub-images using a signal processor to correct fordistortions and alterations introduced by the optical configuration, andcombining the plurality of sub-images into a composite image to providea substantially faithful image of the object.

According to another embodiment, there is an apparatus for microscopyincluding an object plane on which can be disposed a first surface of asubstrate, wherein the substrate is characterized by a homogeneousrefractive index (n_(sub)) and a surface normal. The apparatus formicroscopy can also include a first optical system disposed to providean evanescent wave illumination of the object plane by providing asubstantially coherent illumination of the object plane, theillumination characterized by a wavelength λ and a radius of curvatureand disposed at one of a plurality of incident wave vectors from about2π/λ to about 2πn_(sub)/λ with respect to a surface normal of thesubstrate and at a multiplicity of azimuth angles spanning 0 to 2π,wherein the plurality of incident wave vectors correspond to anglesbeyond a total internal reflection angle θ_(c) of the substrate. Theapparatus for microscopy can further include a second optical systemdisposed to collect portions of the illumination scattered from theobject plane, the second optical system having an optical axis disposedat one of a plurality of center wave vectors from about 0 to about 2π/λ,with respect to the substrate surface normal and at the azimuth anglecorresponding to the illumination of the first optical system, whereinthe second optical system is characterized by a numerical aperture (NA).The apparatus for microscopy can also include a third optical systemdisposed in an optical path of the first optical system to provideinterferometric reintroduction of a portion of the coherent illumination(reference beam) into the second optical system, wherein each of anamplitude, a phase, a radius of curvature and an angle of incidence ofthe reference is adjusted as required such that a corrected referencewave is present at the image plane of the second optical system. Theapparatus for microscopy can further include an electronic image devicedisposed at an image plane of the second optical system that respondslinearly to the local optical intensity and transfers the local opticalintensity map across the image plane (a sub-image) to a signal processordevice in electronic form, a device for adjusting the first, the second,and the third optical systems to collect sub-images for different pairsof the pluralities of incident (first optical system) and collectioncenter (second optical system) wave vectors so as to sequentially obtaina plurality of sub-images corresponding to a plurality of regions ofspatial frequency space, and an electronic device to sequentiallyreceive the electronic form of the sub-images and manipulate thesub-images to correct for distortions and alterations introduced by theoptical configuration, store, and combine the plurality of sub-imagescorresponding to the plurality of regions of spatial frequency space tocreate a composite image. According to yet another embodiment, there isa method for microscopy including providing an object disposed over asurface of a planar substrate characterized by a homogeneous refractiveindex (n_(sub)) and a surface normal. The method for microscopy can alsoinclude providing a first optical system disposed to provide anevanescent wave illumination of the object plane by providing asubstantially coherent illumination of the object plane, theillumination characterized by a wavelength λ and a radius of curvatureand disposed at one of a plurality of incident wave vectors from about λto about 2πn_(sub)/λ with respect to a surface normal of the substrateand at a multiplicity of azimuth angles spanning 0 to 2π, wherein theplurality of incident wave vectors correspond to angles beyond a totalinternal reflection angle θ_(c) of the substrate. The method formicroscopy can further include providing a second optical system havingan optical axis disposed at one of a plurality of center wave vectorsfrom about 0 to about 2π/λ with respect to the surface normal, whereinthe second optical system is characterized by a numerical aperture (NA)and providing a third optical system disposed in an optical path of thefirst optical system to provide interferometric reintroduction of aportion of the coherent plane wave illumination (reference beam) intothe second optical system, wherein the amplitude, phase, and position ofthe reintroduced illumination plane wave in the back focal plane of thesecond optical system is adjusted as required. The method for microscopycan also include recording a sub-image of the object at an object planeusing an electronic image device, wherein the sub-image is formed as aresult of interference of the coherent plane wave illumination of theobject and the reference beam, adjusting the first, the second, and thethird optical systems to sequentially collect a plurality of sub-imagescorresponding to a plurality of regions of spatial frequency space,manipulating each of the plurality of sub-images using a signalprocessor to correct for distortions and alterations introduced by theoptical configuration, and combining the plurality of sub-images into acomposite image to provide a substantially faithful image of the object.

In accordance with another embodiment, there is an apparatus formicroscopy including an object plane on which can be disposed a firstsurface of a planar substrate, wherein the substrate is characterized bya homogeneous refractive index (n_(sub)) and a surface normal. Theapparatus can also include a first optical system disposed to provide asubstantially coherent illumination of the object plane, theillumination characterized by a wavelength λ and a radius of curvatureand disposed at one of a plurality of incident wave vectors from about 0to about 2πn_(sub)/λ with respect to a surface normal of the substrateand at a plurality of azimuth angles spanning 0 to 2π. The apparatus canfurther include at least one grating on the side of the substrateopposite the object plane, each grating characterized by a period, adepth, a grating profile and a position to further scatter reflectedwaves resulting from the coherent illumination of the object plane intopropagating waves in the medium below the substrate and a second opticalsystem having an optical axis disposed at one of a plurality of centerwave vectors from about 0 to about 2π/λ with respect to the surfacenormal, wherein the second optical system can include the gratings onthe second side of the substrate and is characterized by a numericalaperture (NA). The apparatus for microscopy can also include a thirdoptical system disposed in an optical path of the first optical systemto provide interferometric reintroduction of a portion of the coherentillumination (reference beam) into the second optical system, whereineach of an amplitude, a phase, a radius of curvature and an angle ofincidence of the reference is adjusted as required such that a correctedreference wave is present at the image plane of the second opticalsystem. The apparatus for microscopy can further include an electronicimage device disposed at an image plane of the second optical systemthat responds linearly to the local optical intensity and transfers thelocal optical intensity map across the image plane (a sub-image) to asignal processor device in electronic form, a device for adjusting thefirst, the second, and the third optical systems to collect sub-imagesfor different pairs of the pluralities of incident (first opticalsystem) and collection center (second optical system) wave vectors so asto sequentially obtain a plurality of sub-images corresponding to aplurality of regions of spatial frequency space, and an electronicdevice to sequentially receive the electronic form of the sub-images andmanipulate the sub-images to correct for distortions and alterationsintroduced by the optical configuration, store, and combine theplurality of sub-images corresponding to the plurality of regions ofspatial frequency space to create a composite image.

In accordance with yet another embodiment, there is a method formicroscopy including providing an object disposed over a first side of aplanar substrate, the substrate characterized by a homogeneousrefractive index (n_(sub)) and a surface normal such that the object isseparated from the substrate by a distance of about ≦λ and providing atleast one grating on a second side of the substrate opposite the firstside, each grating characterized by a position, a period, a depth, and agrating profile, wherein the at least grating further scatters reflectedwaves resulting from the coherent illumination of the object intopropagating waves in the medium below the substrate. The method formicroscopy can also include providing a first optical system disposed toprovide a substantially coherent illumination of the object plane, theillumination characterized by a wavelength λ and a radius of curvatureand disposed at one of a plurality of incident wave vectors from about 0to about 2πn_(sub)/λ with respect to a surface normal of the substrateand at a plurality of azimuth angles spanning about 0 to about 2π andproviding a second optical system having an optical axis disposed at oneof a plurality of center wave vectors from about 0 to about 2π/λ withrespect to the surface normal, wherein the second optical system caninclude the at least one grating on the second side of the substrate andis characterized by a numerical aperture (NA). The method for microscopycan further include providing a third optical system disposed in anoptical path of the first optical system to provide interferometricreintroduction of a portion of the coherent illumination (referencebeam) into the second optical system, wherein each of an amplitude, aphase, a radius of curvature and an angle of incidence of the referenceis adjusted as required such that a corrected reference wave is presentat the image plane of the second optical system and recording asub-image of the object at an object plane using an electronic imagedevice, wherein the sub-image is formed as a result of interferencebetween the scattering resulting from the coherent illumination of theobject and the reference beam. The method for microscopy can alsoinclude adjusting the first, the second, and the third optical systemsto sequentially collect a plurality of sub-images corresponding to aplurality of regions of spatial frequency space, manipulating each ofthe plurality of sub-images using a signal processor to correct fordistortions and alterations introduced by the optical configuration, andcombining the plurality of sub-images into a composite image to providea substantially faithful image of the object.

According to various embodiments, there is an apparatus for coherentanti-Stokes Raman (CARS) microscopy including an object plane on whichcan be disposed a first surface of a planar substrate, wherein thesubstrate is characterized by a homogeneous refractive index (n_(sub))and a surface normal. The apparatus for CARS microscopy can include afirst optical system disposed to provide a illumination of the objectplane, the illumination characterized by two substantially coincidentcoherent beams with wavelengths λ1 and λ2 and corresponding angularfrequencies ω1 and ω2 with ω1>ω2, a radius of curvature, and disposed atone of a plurality of incident wave vectors from about 0 to about2πn_(sub)/λ₁ with respect to a surface normal of the substrate and at aplurality of azimuth angles spanning about 0 to about 2π and a secondoptical system (collection) having an optical axis disposed at one of aplurality of center wave vectors from about 0 to about 2πn_(sub)/λ₁ withrespect to the surface normal, wherein the second optical system ischaracterized by a numerical aperture (NA) and is responsive primarilyto optical signals at frequencies greater than ω₁. The apparatus forCARS microscopy can also include a third optical system disposed in anoptical path of the first optical system to provide interferometricreintroduction of a reference illumination (reference beam) at afrequency of 2ω₁−ω₂, into the second optical system, wherein each of anamplitude, a phase, a radius of curvature and an angle of incidence ofthe reference is adjusted as required such that a corrected referencewave is present at the image plane of the second optical system and anelectronic image device disposed at an image plane of the second opticalsystem that responds linearly to the local optical intensity andtransfers the local optical intensity map across the image plane (asub-image) to a signal processor device in electronic form. Theapparatus for CARS microscopy can further include a device for adjustingthe first, the second, and the third optical systems to collectsub-images for different pairs of the pluralities of incident (firstoptical system) and collection center (second optical system) wavevectors so as to sequentially obtain a plurality of sub-imagescorresponding to a plurality of regions of spatial frequency space andan electronic device to sequentially receive the electronic form of thesub-images and manipulate the sub-images to correct for distortions andalterations introduced by the optical configuration, store, and combinethe plurality of sub-images corresponding to the plurality of regions ofspatial frequency space to create a composite image.

According to another embodiment, there is a method for coherentanti-Stokes Raman (CARS) microscopy including providing an object atopan object plane disposed upon a planar substrate, wherein the substrateis characterized by a homogeneous refractive index (n_(sub)) and asurface normal. The method for CARS microscopy can include providing afirst optical system disposed to provide a illumination of the objectplane, the illumination characterized by two substantially coincidentcoherent beams with wavelengths λ₁ and λ₂ and corresponding angularfrequencies ω₁ and ω₂ with ω₁>ω₂, a radius of curvature, and disposed atone of a plurality of incident wave vectors from about 0 to about2πn_(sub)/λ₁ with respect to a surface normal of the substrate and at amultiplicity of azimuth angles spanning 0 to 2π and providing a secondoptical system (collection) having an optical axis disposed at one of aplurality of center wave vectors from about 0 to about 2πn_(sub)/λ₁ withrespect to the surface normal, wherein the second optical system ischaracterized by a numerical aperture (NA) and is responsive primarilyto optical signals at frequencies greater than ω₁. The method for CARSmicroscopy can further include providing a third optical system disposedin an optical path of the first optical system to provideinterferometric reintroduction of a reference illumination (referencebeam) at a frequency of 2ω₁−ω₂, into the second optical system, whereineach of an amplitude, a phase, a radius of curvature and an angle ofincidence of the reference is adjusted as required such that a correctedreference wave is present at the image plane of the second opticalsystem and recording a sub-image of the object at an object plane usingan electronic image device, wherein the sub-image is formed as a resultof interference between the scattering resulting from the coherentillumination of the object and the reference beam. The method for CARSmicroscopy can also include adjusting the first, the second, and thethird optical systems to sequentially collect a plurality of sub-imagescorresponding to a plurality of regions of spatial frequency space,manipulating each of the plurality of sub-images using a signalprocessor to correct for distortions and alterations introduced by theoptical configuration, and combining the plurality of sub-images into acomposite image to provide a substantially faithful image of the object.

Additional objects and advantages of the invention will be set forth inpart in the description which follows, and in part will be obvious fromthe description, or may be learned by practice of the invention. Theobjects and advantages of the invention will be realized and attained bymeans of the elements and combinations particularly pointed out in theappended claims.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not restrictive of the invention, as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate several embodiments of theinvention and together with the description, serve to explain theprinciples of the invention.

FIG. 1 shows an exemplary prior art imaging interferometric microscopy(IIM) experimental arrangement.

FIG. 2A shows the frequency space coverage for conventional normalincidence coherent illumination.

FIG. 2B shows the frequency space coverage for an off-axis incidencecoherent illumination.

FIG. 3 shows an exemplary structured illumination approach to IIM,according to various embodiments of the present teachings.

FIG. 4 shows the schematic of structural illumination and restorationalgorithms, in accordance with the present teachings.

FIG. 5A is a schematic illustration showing a dynamic physical block ina back pupil plane of the second optical system to alternately block andunblock the reference beam, according to present teachings.

FIG. 5B is a schematic illustration showing injection of the referencebeam into a second optical system using a prism, according to presentteachings.

FIG. 5C is a schematic illustration of injection of the reference beaminto a second optical system using a beamsplitter, according to presentteachings.

FIG. 5D is a schematic illustration showing blocking of the referencebeam with a k-vector filter, according to present teachings.

FIG. 5E is a schematic illustration showing injection of the referencebeam with a grating, according to present teachings.

FIG. 6 shows k-vector filter characteristic of an exemplary SiN-on-glassguided mode resonance filter.

FIG. 7A shows the frequency space coverage for the arrangement of FIG.3, with intermediate frequency offset within bandpass of lens.

FIG. 7B shows the frequency space coverage for the arrangement of FIG. 3after removal of the dark field and intermediate frequency imaging termsand correction of the observed frequencies.

FIG. 8A schematically illustrates a Manhattan geometry pattern used forimage resolution exploration consisting of five nested “ells” and alarge box.

FIG. 8B illustrates intensity Fourier space components of the Manhattangeometry pattern shown in FIG. 8A, mapped onto a frequency spacecoverage of the imaging system.

FIGS. 9A-9F show the preliminary results of an experiment using an NA0.4 objective with a He—Ne laser illumination (λ=633 nm) and with about240 nm structure with corresponding simulations using the configurationpresented in FIG. 5A.

FIG. 10A shows reconstructed images of 260 nm and 240 nm CD structuresobtained using the optical configuration of FIG. 5A after the dark fieldsubtraction, frequency shifting correction, and sub-image combination.

FIG. 10B show a crosscut (gray) of the images of FIG. 10A compared witha crosscut of corresponding simulation (black).

FIG. 11A shows reconstructed images of 260 nm and 240 nm CD structuresobtained using the optical arrangement shown in FIG. 5E.

FIG. 11B shows a crosscut (gray) of the images of FIG. 10A compared witha crosscut of corresponding simulation (black).

FIG. 12A shows an exemplary IIM arrangement with evanescentillumination, according to various embodiments of the present teachings.

FIG. 128 shows an exemplary IIM arrangement with evanescent illuminationwith a rotated optical axis, according to various embodiments of thepresent teachings.

FIGS. 13A-13C show alternate approaches for coupling light for substrateillumination, in accordance with various embodiments.

FIG. 14A schematically illustrates Manhattan geometry pattern used forimage resolution exploration consisting of five nested “ells” and alarge box.

FIG. 14B illustrates intensity Fourier space components of the Manhattangeometry pattern shown in FIG. 14A, mapped onto a frequency spacecoverage of the imaging system, for a structure with CD=180 nm for theoptical arrangement shown in FIG. 3.

FIG. 14C illustrates intensity Fourier space components of the Manhattangeometry pattern shown in FIG. 12A, mapped onto a frequency spacecoverage of the imaging system, for a structure with CD=150 nm for theoptical arrangement shown in FIG. 11A.

FIG. 15A show reconstructed image of 260 nm and 240 nm CD structuresobtained using the optical arrangement shown in FIG. 12A.

FIG. 15B show a crosscut (gray) of the images of FIG. 15A compared witha crosscut of corresponding simulation (black).

FIG. 16A shows a reconstructed high frequency image of a 150 nmstructure using evanescent illumination and a tilted optical system,shown in FIG. 12B.

FIG. 16B shows a high frequency image simulation of a 150 nm structureusing evanescent illumination and a tilted optical system, shown in FIG.12B.

FIG. 16C shows experimental and simulation cross-cuts of images shown inFIGS. 16A and 16B.

FIG. 16D shows a reconstructed composite image of a 150 nm structureusing evanescent illumination and a tilted optical system, shown in FIG.12B

FIG. 16E shows a composite image simulation of a 150 nm structure usingevanescent illumination and a tilted optical system, shown in FIG. 12B.

FIG. 16F shows experimental and simulation cross-cuts of images shown inFIGS. 16D and 16E.

FIG. 17 shows available frequency space coverage for various IIM opticalconfigurations, in accordance with the present teachings.

FIG. 18 shows a schematic diagram showing the high angle light scatteredfrom an object and extracted from the substrate using at least onegrating, in accordance with various embodiments of the presentteachings.

FIG. 19 shows prism coupling for extracting light scattered into asubstrate, in accordance with various teachings.

FIGS. 20A and 20B show embodiments for tiling frequency space with asubstrate (n=1.5) in one direction, in accordance with variousembodiments.

FIG. 21 show an exemplary tiling with almost complete frequency spacecoverage (NA=0.65, n=1.5), in accordance with present teachings.

FIG. 22 show another exemplary tiling with a larger NA objective lens(NA=0.95, n=1.5), in accordance with various embodiments.

FIG. 23 show another exemplary tiling strategy for high index substrate(n=3.6, collection NA=0.65, as in FIG. 18), in accordance with variousembodiments.

DESCRIPTION OF THE EMBODIMENTS

Reference will now be made in detail to the present embodiments,examples of which are illustrated in the accompanying drawings. Whereverpossible, the same reference numbers will be used throughout thedrawings to refer to the same or like parts.

Notwithstanding that the numerical ranges and parameters setting forththe broad scope of the invention are approximations, the numericalvalues set forth in the specific examples are reported as precisely aspossible. Any numerical value, however, inherently contains certainerrors necessarily resulting from the standard deviation found in theirrespective testing measurements. Moreover, all ranges disclosed hereinare to be understood to encompass any and all sub-ranges subsumedtherein. For example, a range of “less than 10” can include any and allsub-ranges between (and including) the minimum value of zero and themaximum value of 10, that is, any and all sub-ranges having a minimumvalue of equal to or greater than zero and a maximum value of equal toor less than 10, e.g., 1 to 5. In certain cases, the numerical values asstated for the parameter can take on negative values. In this case, theexample value of range stated as “less that 10” can assume negativevalues, e.g. −1, −2, −3, −10, −20, −30, etc.

FIG. 1 shows a prior art imaging interferometric microscopy (IIM)arrangement 100. As shown in FIG. 1, a collimated (equivalent tocoherent) illumination beam 110 is incident on an object 120 at an angleof incidence θ. In the illustrated case, θ is beyond the collectionangle of the objective lens 130 and an auxiliary optical system 135 isshown schematically to collect the zero-order transmission 109,appropriately adjust its divergence, direction, and phase and re-injectit onto the image plane 124 where it interferes with the diffractedbeams 101, 102, 103, 104 from the object 120 to construct a partialimage. Alternatively, instead of using the zero-order transmission 109,which might be blocked by the objective-lens 130 mount, a portion of theillumination beam 110 can be split off before the object 120 anddirected around the objective lens 130. The interference between thezero-order beam 109 and the diffracted beams 101, 102, 103, 104transmitted through the objective lens 130 can shift the collecteddiffracted information back to high frequency. As a result of thesquare-law intensity response, the resulting frequency coverage 140B canbe represented by a pair of circles 144, 146 of radius NA/λ shifted awayfrom zero frequency 142 by 2(2π)NA/λ as shown in FIG. 2B. FIG. 2B showsthe frequency space coverage 140B for off-axis coherent illumination,where frequencies beyond the lens bandpass are recorded in the sub-imageas a result of the interferometric reconstruction. For comparison, FIG.2A shows the frequency space coverage 140A for conventional normalincidence on-axis coherent illumination.

An object of the present teachings is to reduce or eliminate therequirement of the prior art for optical access to between the back ofthe objective lens and the image plane of the second optical system.This access is required for injecting the reference beam 109 in theprior art (FIG. 1). However, in many existing optical microscopes, thisregion is inaccessible. The structured illumination approach disclosedherein provides alternative methods of injecting the reference beam infront of the objective lens of the second optical system, therebysimplifying the application of imaging interferometric microscopy toexisting optical microscopy systems. Since both the diffracted beams andthe reference beams are not transmitted through the same objective,characterized by an NA, the high frequency image components arenecessarily shifted to lower frequency. This is similar to the use of anintermediate frequency in heterodyne radio receivers, but in the spatialfrequency rather than the temporal frequency domain. It is necessary toreset the spatial frequencies by signal processing after each sub-imageis captured in the electronic recording device. Additional advantages ofthis approach are that the pixel count requirements in the image planeare reduced, since only lower spatial frequencies, up to 2(2π)NA/λ, arerecorded, and the interferometer can be made smaller since all of thecomponents are on the front side of the objective lens, reducingvibrational effects on the interferometric reconstruction.

FIG. 3 shows an optical arrangement of the apparatus 200 for anexemplary structured illumination approach to IIM, according to variousembodiments of the present teachings. The apparatus 200 can include anobject plane 222 on which a first surface of a substrate 225 can bedisposed, wherein the substrate 225 can be characterized by ahomogeneous refractive index (n_(sub)) and a surface normal 226. Theapparatus 200 can also include a first optical system (not shown)disposed to provide a substantially coherent illumination 210 of theobject plane 222, the illumination 210 characterized by a wavelength λand a radius of curvature and disposed at one of a plurality of incidentwave vectors from about 0 to about 2π/λ with respect to a surface normalof the substrate and at a plurality of azimuth angles spanning 0 to 2π.The apparatus 200 can also include a second optical system 230 disposedto collect portions of the illumination scattered from the object plane222, the second optical system having an optical axis 236 disposed atone of a plurality of center wave vectors from about 0 to about 2π/λwith respect to the substrate surface normal 226 and at the azimuthangle corresponding to the illumination of the first optical system,wherein the second optical system 230 is characterized by a numericalaperture (NA). In various embodiments, the second optical system 230 caninclude at least one objective lens. The apparatus 200 can also includea third optical system disposed between the optical path of the firstoptical system and an entrance aperture of the second optical system toprovide interferometric reintroduction of a portion of the coherentillumination (reference beam) 210′ into the second optical system 230,wherein each of an amplitude, a phase, a radius of curvature, and anangle of incidence of the reference beam can be adjusted such that acorrected reference beam can be present at the image plane 224 of thesecond optical system 230. The reference beam 21′ is obtained bysplitting off a portion of the illumination beam 210 and the apparatus200 is configured so that the total path lengths of the illuminationbeam 210 and the reference beam 210′ from the beam splitter to the imageplane 224 are within the temporal coherence length of the source toinsure interferometric reconstruction of the sub-image. The apparatuscan also include an electronic image device 228 disposed at the imageplane 224 of the second optical system 230 that responds linearly to thelocal optical intensity and transfers the local optical intensity mapacross the image plane (a sub-image) to a signal processor device inelectronic form. In various embodiments, the electronic image device 228can be a charged coupled device (CCD) camera, a CMOS (complementarymetal-oxide semiconductor) camera, and any similar electronic focalplane array device. The apparatus 200 can further include a device foradjusting the first, the second, and the third optical systems tocollect sub-images for different pairs of the pluralities of incident(first optical system) and collection center (second optical system)wave vectors so as to sequentially obtain a plurality of sub-imagescorresponding to a plurality of regions of spatial frequency space. Invarious embodiments, the device can block/unblock various beams, rotatesubstrate etc. In some embodiments, the device can include mechanicalcomponents, such as, for example, motors. In other embodiments, thedevice can include electronic components, such as, for example, acousticmodulators or similar devices. The apparatus 200 can further include anelectronic device to sequentially receive the electronic form of thesub-images and manipulate the sub-images to correct for distortions andalterations introduced by the optical configuration, store, and combinethe plurality of sub-images corresponding to the plurality of regions ofspatial frequency space to create a composite image. In some otherembodiments, the electronic device can include one or more computers. Insome embodiments, the first, the second, and the third optical systemscan be arranged in a transmission configuration with respect to thesubstrate surface. In other embodiments, the first, the second, and thethird optical systems can be arranged in a reflection configuration withrespect to the substrate surface.

In certain embodiments apparatus 200 for an exemplary structuredillumination approach to IIM can also include at least one knownreference object to cover a small part of the image field.

According to various embodiments, there is a method for structuralimaging interferometric microscopy. The method can include providing anobject 220 disposed over a planar substrate 225, wherein the substrate225 is characterized by a homogeneous refractive index (n_(sub)) and asurface normal 226 and providing a first optical system to illuminatethe object 220 with substantially coherent illumination 210, theillumination characterized by a wavelength λ and a radius of curvatureand disposed at one of a plurality of incident wave vectors from about 0to about 2π/λ with respect to a surface normal of the substrate and at amultiplicity of azimuth angles spanning from about 0 to about 2λ. Themethod can also include providing a second optical system 230 disposedto collect portions of the illumination scattered from the object plane222, the second optical system 230 having an optical axis 236 disposedat one of a plurality of center wave vectors from about 0 to about 2π/λwith respect to the substrate 225 surface normal 226 and at the azimuthangle corresponding to the illumination of the first optical system,wherein the second optical system 230 is disposed such that the object220 is substantially at the object plane 222 of the second opticalsystem 230 which is characterized by a numerical aperture (NA). Themethod can further include providing a third optical system disposedbetween the optical path of the first optical system and an entranceaperture of the second optical system to provide interferometricreintroduction of a portion of the coherent illumination (referencebeam) 210′ into the second optical system, wherein each of an amplitude,a phase, a radius of curvature and an angle of incidence of thereference can be adjusted such that a corrected reference wave ispresent at the image plane of the second optical system, wherein thecorrected reference beam 210′ and the illumination beam 210 are withinthe temporal coherence length of the source. The method can also includerecording a sub-image of the object 220 at an object plane 222 using anelectronic image device 228, wherein the sub-image is formed as a resultof interference between the scattering resulting from the coherentillumination of the object 220 and the reference beam 210′. The methodcan also include adjusting the first, the second, and the third opticalsystems to sequentially collect a plurality of sub-images correspondingto a plurality of regions of spatial frequency space, manipulating eachof the plurality of sub-images using a signal processor to correct fordistortions and alterations introduced by the optical configuration, andcombining the plurality of sub-images into a composite image to providea substantially faithful image of the object 220. In variousembodiments, the method can further include one or more processes ofsubtraction of dark field images, subtraction of background images,shifting of spatial frequencies in accordance with the opticalconfiguration, and elimination of one or more overlapping coverages ofthe frequency space wherein the elimination operations can be performedeither in the optical systems or in the signal processing. In someembodiments, the method can also include selecting the regions ofspatial frequency space to provide a more or less faithful image of theobject 220 in the object plane 222. One of ordinary skill in the artwould know that the regions of frequency space that are important varydepending on the object. For example for a Manhattan geometry pattern,there is less need to gather spectral information on the diagonals. See,for example, Neumann et al. in Optics Express, Vol. 16, No. 10, 2008 pp6785-6793 which describes a structural illumination for the extension ofimaging interterometric microscopy, the disclosure of which isincorporated by reference herein in its entirety.

FIG. 4 shows a flow diagram schematic of structural illumination andrestoration algorithms. High spatial frequencies represented bydiffracted beams from the off-axis illumination are mixed with the localoscillator beam, the dark field of the image is subtracted as is the lowfrequency image without its dark field. Then the spatial frequencies arereset in Fourier space and the whole image is reconstructed by combininghigh and low frequency sub-images.

To mathematically explain the structured illumination approach to IIM,first a simple mathematical description of a conventional coherentillumination microscopy image will be described and then themathematical description will be extended to the prior art IIMexperiment and finally to the structured illumination approach.

The total transmission through an arbitrary object (assumed to beperiodic on large scale to allow Fourier sums rather than Fourierintegrals) and illuminated by a plane wave at normal incidence can begiven by:

$\begin{matrix}{{\sum\limits_{{\forall k},{l \in R}}{A_{k,l}{\exp \left\lbrack {{\; {xk}\; \omega_{x}} + {\; {yl}\; \omega_{y}}} \right\rbrack}^{\; \gamma_{k,l}z}}} = {{A_{0,0}^{\; \gamma_{0,0}z}} + {\sum\limits_{k,{l \neq 0}}{A_{k,l}{\exp \left\lbrack {{\; {xk}\; \omega_{x}} + {\; {yl}\; \omega_{y}}} \right\rbrack}^{\; \gamma_{k,l}z}}}}} & (1)\end{matrix}$

where ω_(x), ω_(y) are the discrete spatial frequency increments of theFourier summation; x and y are orthogonal spatial coordinates;

$\gamma_{k,l} \equiv \sqrt{\left( \frac{2\; \pi \; n}{\lambda} \right)^{2} - \left( {k\; \omega_{x}} \right)^{2} - \left( {l\; \omega_{y}} \right)^{2}}$

with n the refractive index of the transmission medium (1 for air); R isthe set of integers, for which (|γ_(k,l)|)²>0, that is the range ofintegers for which the diffracted beams are within the bandpass of thetransmission medium and are propagating in the z-direction, away fromthe object. Note that this representation is a scalar approximation thatis appropriate as long as the angles do not get too large, and it isassumed below that all beams are polarized in the same direction. A morerigorous treatment is straightforward, but mathematically gets morecomplex and obscures the physical insight in these simpler equations.

The transmission through the optical system adds a filter factor:

$\begin{matrix}{{{T\left( {0;0} \right)}A_{0,0}^{\; \gamma_{0,0}z}} + {\sum\limits_{k,{l \neq 0}}{{T\left( {{k\; \omega_{x}};{l\; \omega_{y}}} \right)}A_{n,l}{\exp \left\lbrack {{\; {x\left( {k\; \omega_{x}} \right)}} + {\; {yl}\; \omega_{y}}} \right\rbrack}^{\; \gamma_{k,l}z}}}} & (2)\end{matrix}$

The transmission function of the objective lens is a simple bandpassfunction:

$\begin{matrix}\begin{matrix}{{T\left( {\omega_{X};\omega_{Y}} \right)} = {{1\mspace{14mu} {for}\mspace{14mu} \sqrt{\omega_{X}^{2} + \omega_{Y}^{2}}} \leq \omega_{MAX}}} \\{= \frac{2\; \pi \; {NA}}{\lambda}} \\{{= {0\mspace{14mu} {else}}},}\end{matrix} & (3)\end{matrix}$

and the final image intensity can be obtained by taking the squaremodulus of equation 2, viz:

$\begin{matrix}{{I\left( {x,y,z} \right)} = {{\left\lbrack {T\left( {0,0} \right)} \right\rbrack^{2}{A_{0,0}}^{2}} + {\sum\limits_{k,l}{{T\left( {0,0} \right)}{T\left( {{k\; \omega_{x}},{l\; \omega_{y}}} \right)}A_{0,0}A_{k,l}^{*}{\exp \left\lbrack {- {\iota \left( {{k\; \omega_{x}x} + {l\; \omega_{y}y}} \right)}} \right\rbrack}^{{{({\gamma_{0,0} - \gamma_{k,l}})}}z}}} + {c.c.{+ {\sum\limits_{k,l}{\sum\limits_{k^{\prime},l^{\prime}}{{T\left( {{k\; \omega_{x}},{l\; \omega_{y}}} \right)}{T\left( {{k^{\prime}\; \omega_{x}},{l^{\prime}\; \omega_{y}}} \right)}A_{k,,l}A_{k^{\prime},l^{\prime}}^{*}\exp \left\{ {\left\lbrack {{\left( {k - k^{\prime}} \right)\omega_{x}x} + {\left( {l - l^{\prime}} \right)\; \omega_{y}y}} \right\rbrack} \right\} ^{{{({\gamma_{k,l} - \gamma_{k^{\prime},l^{\prime}}})}}z}}}}}} + {c.c}}} & (4)\end{matrix}$

Each of the three lines in this result has a simple physicalinterpretation. The top line is a constant independent of spatialcoordinates, equal to the average intensity of the pattern. This ensuresthat the intensity is always positive as physically required. The secondline represents the imaging terms that we want to retain. Finally thethird line is the cross-correlation of the diffracted beams withthemselves equivalent to the dark field image that would be obtained ifthe zero-order diffraction (transmission) was blocked at the back pupilplane. The imaging terms are band-limited to transverse spatialfrequencies of (2π/λ)NA; the dark field terms extend out to (4π/λ)NA andare typically weaker in intensity than the imaging terms since for anobject with thickness<<λ, |A_(0,0)| is larger than any of the diffractedterms. In all of the summations the summation indices extend over allterms in R except for the zero-order term which has been explicitlyseparated. Equation 4 gives the intensity over all space beyond theobjective lens. The image is obtained in the back image plane (z=0)where the exponentials in γz vanish. The focusing information iscontained in these exponential terms and its characteristic length, thedepth-of-field, depends on the NA, as is well known. A Fourier opticsperspective provides additional insight into the three terms. The DCterm (top line) is a δ-function at the origin. The image terms fill acircle of radius 2πNA/λ as a result of the band-limited transmissionfunction. Finally, the dark-field image contains frequencies up to4πNA/λ as a result of the interference of the various diffracted orders.

It is well-known that additional, higher spatial frequency, informationcan be accessed with off-axis illumination. FIG. 1 shows a conventionalIIM arrangement 100, wherein a collimated illumination beam 110 can beincident on an object 120 at an angle of incidence θ. In particular inthe case of IIM, the offset angle is chosen such that the zero-ordertransmission (reflection) is beyond the lens (130) NA,

$\omega_{offset} > {\frac{2\; \pi \; {NA}}{\lambda} \cdot}$

The result is that higher spatial frequency information is transmittedthrough the lens, but only a dark field image is recorded in atraditional coherent illumination microscopy configuration (without thereference beam 109). This is solved in IIM by introducing an auxiliaryoptical system 135, an interferometer that reinjects the zero-ordertransmission on the low-NA side of the lens to reset the spatialfrequencies. In practice it is simpler to reintroduce the zero-ordertransmission as an appropriately mode matched point source in the backpupil plane without actually using the transmitted beam which is oftenblocked by the objective lens mount. Effectively, the interferometerresults in a modified filter transfer function where the zero-order istransmitted even though it is outside the lens NA. The amplitude, thephase, and the offset position in the back focal plane of the objectivehave to be controlled to provide a correct sub-image. These are oftenset by using a nearby, known reference object along with the object ofinterest.

It is straightforward to extend the mathematical treatment to theoff-axis illumination case. Equation 2 can be modified to:

$\begin{matrix}{{A_{0,0}^{\prime}^{{- }\; \omega_{off}x}^{{i{(\gamma_{0,0}^{\prime})}}z}} + {\sum\limits_{k,{l \neq 0}}{{T\left( {{{k\; \omega_{x}} - \omega_{off}};{l\; \omega_{y}}} \right)}A_{n,l}{\exp \begin{bmatrix}{{\; x\left( {{k\; \omega_{x}} - w_{off}} \right)} +} \\{\; l\; \omega_{y}y}\end{bmatrix}}^{\; {\gamma^{\prime}}_{k,l}z}}}} & (5)\end{matrix}$

where ω_(off)=2π sin(θ_(off))/λ is the frequency offset arising from theoff-axis illumination at angle θ_(off) (assumed in the x-direction), theprimes on the γs indicate that the propagation directions take intoaccount the offset illumination, and the prime on the A_(0,0) refers tothe re-injected O-order.

Taking the square of equation 5 can provide the intensity on the imagingcamera:

$\begin{matrix}\begin{matrix}{{A_{0,0}^{*}}^{2} +} & \ldots & \left( {{dc}\mspace{14mu} {offset}} \right) \\{{\sum\limits_{k,{l \neq 0}}{A_{0,0}^{\prime}A_{k,l}^{*}{T\begin{pmatrix}{{{k\; \omega_{x}} - \omega_{off}};} \\{l\; \omega_{y}}\end{pmatrix}}{\exp \begin{bmatrix}{{\; k\; \omega_{x}x} +} \\{\; l\; \omega_{y}y}\end{bmatrix}}^{{{({\gamma_{0,0}^{\prime} - y_{k,l}})}}z}}} + {c.c. +}} & \ldots & ({imaging}) \\\begin{matrix}{\sum\limits_{k,{l \neq 0^{\prime}}}{\sum\limits_{k^{\prime},{l^{\prime} \neq 0}}{A_{k,l}{T\left( {{{k\; \omega_{x}} - \omega_{off}};{l\; \omega_{y}}} \right)}A_{n^{\prime},l^{\prime}}^{*}{T\left( {{{k^{\prime}\omega_{x}} - \omega_{off}};{l^{\prime}\omega_{y}}} \right)}}}} \\{{\exp \begin{bmatrix}{{\; \left( {k - k^{\prime}} \right)\omega_{x}x} +} \\{{\left( \; {l - l^{\prime}} \right)}\; \omega_{y}y}\end{bmatrix}}^{{{({\gamma_{k,l}^{\prime} - {y^{\prime}}_{k^{\prime},l^{\prime}}})}}z}}\end{matrix} & \ldots & \left( {{dark}\mspace{14mu} {field}} \right)\end{matrix} & (6)\end{matrix}$

where the three terms on separate lines correspond to (top) a constantterm, (middle) the imaging terms and (bottom) the dark field image.Subtracting out the dark field terms (by taking an image with theinterferometer blocked so that only the third term survives) provides asub-image that accurately captures the spatial frequency components thatare transmitted through the optical system. Note that the imaging terms(middle line) are at the correct frequencies and that the offsetillumination angle has cancelled out of the expression except for thefilter transmission functions.

Changing both the illumination angle (and the angle of reintroduction)and the azimuthal angle changes the offset allowing recording of adifferent region of frequency space. Specifically, for Manhattangeometry (x,y oriented patterns) a second offset exposure to capture thehigh spatial frequencies in the y-direction, that is with the substraterotated by π/2, can be used. Additional spatial frequency terms can becaptured with large illumination angles.

Referring back to the FIG. 3, in the exemplary structured illuminationapproach to IIM, there can be two coherent illumination beams 210, 210′,the first beam 210 can be at the same offset as in the previous exampleso that ω_(offset) is > NA/λ, and the second beam 210′ can be at themaximum offset that fits through the lens ω_(off)≦NA/λ, denoted asω_(NA) in the equation. Then the fields are:

$\begin{matrix}{{A_{0,0}{\exp \left( {{- }\; \omega_{off}x} \right)}^{\; \gamma_{0,0}^{off}z}} + {\sum\limits_{k,{l = 0}}{A_{k,l}{\exp \left\lbrack {{{\left( {{k\; \omega_{x}} - \omega_{off}} \right)}x} + {\; l\; \omega_{y}y}} \right\rbrack}^{\; \gamma_{k,l}^{off}z}}} + {B_{0,0}{\exp \left( {{- }\; \omega_{NA}x} \right)}^{\; \gamma_{0,0}^{NA}}} + {\sum\limits_{p,{r \neq 0}}{B_{p,r}{\exp \left\lbrack {{{\left( {{p\; \omega_{x}} - \omega_{NA}} \right)}x} + {\; r\; \omega_{y}y}} \right\rbrack}^{\; \gamma_{p,r}^{NA}z}}}} & (7)\end{matrix}$

where the series with coefficients A_(k,j) are due to the first offsetbeam (210) and the second series with the coefficients B_(p,q) are dueto the second offset beam (210′) and squaring while taking advantage ofthe fact that without the interferometer the A_(0,0) beam 209 is nottransmitted to the objective image plane while the B_(0,0) beam 209′ istransmitted through the lens 230 gives:

$\begin{matrix}\; & (8) \\{\begin{Bmatrix}{{B_{0,0}}^{2} + {\sum\limits_{p,{r \neq 0}}{B_{0,0}B_{p,r}^{*}{T\begin{pmatrix}{{{p\; \omega_{x}} - \omega_{NA}};} \\{r\; \omega_{y}}\end{pmatrix}}}}} \\{{{\exp \left\lbrack {\begin{pmatrix}{{p\; \omega_{x}x} +} \\{r\; \omega_{y}y}\end{pmatrix}} \right\rbrack}^{{{({\gamma_{0,0}^{NA} - \gamma_{p,r}^{NA}})}}z}} + {c.c. +}} \\{\sum\limits_{p,{r \neq 0}}{\sum\limits_{p^{\prime},{r^{\prime} \neq 0}}{B_{p,r}B_{p^{\prime},r^{\prime}}^{*}{T\begin{pmatrix}{{{p\; \omega_{x}} - \omega_{NA}};} \\{r\; \omega_{y}}\end{pmatrix}}{T\begin{pmatrix}{{{p^{\prime}\; \omega_{x}} - \omega_{NA}};} \\{r^{\prime}\; \omega_{y}}\end{pmatrix}}}}} \\{{\exp \left\lbrack {{{\left( {p - p^{\prime}} \right)}x} + {{\left( {r - r^{\prime}} \right)}y}} \right\rbrack}^{{{({\gamma_{p,r}^{NA} - \gamma_{p^{\prime},r^{\prime}}^{NA}})}}z}}\end{Bmatrix} +} & \lbrack I\rbrack \\{\begin{Bmatrix}{\sum\limits_{k,l}{B_{0,0}A_{k,l}^{*}{T\begin{pmatrix}{{{l\; \omega_{x}} - \omega_{off}};} \\{n\; \omega_{y}}\end{pmatrix}}}} \\{{{\exp \begin{bmatrix}{{{- {\left( {{k\; \omega_{x}} - \omega_{off} + \omega_{NA}} \right)}}x} -} \\{{\omega}_{y}y}\end{bmatrix}}^{{{({\gamma_{0,0}^{NA} - \gamma_{k.l}^{off}})}}z}} + {c.c.}}\end{Bmatrix} +} & \lbrack{II}\rbrack \\\begin{matrix}{\sum\limits_{k,l}{\sum\limits_{k^{\prime},l^{\prime}}{A_{k,l}A_{k^{\prime},l^{\prime}}^{*}{T\begin{pmatrix}{{{k\; \omega_{x}} - \omega_{off}};} \\{l\; \omega_{y}}\end{pmatrix}}{T\begin{pmatrix}{{{k^{\prime}\; \omega_{x}} - \omega_{off}};} \\{l^{\prime}\; \omega_{y}}\end{pmatrix}}}}} \\{{{\exp \begin{bmatrix}{{{\left( {k - k^{\prime}} \right)}\; \omega_{x}x} +} \\{\left( {l - l^{\prime}} \right)\omega_{y}y}\end{bmatrix}}^{{{({\gamma_{k,l}^{off} - \gamma_{k^{\prime},l^{\prime}}^{off}})}}z}} + {c.c.}}\end{matrix} & \lbrack{III}\rbrack \\\begin{matrix}{\sum\limits_{k,l}{\sum\limits_{p,{r \neq 0}}{A_{k,l}B_{p,r}^{*}{T\begin{pmatrix}{{{k\; \omega_{x}} - \omega_{off}};} \\{l\; \omega_{y}}\end{pmatrix}}{T\begin{pmatrix}{{{p\; \omega_{x}} - \omega_{NA}};} \\{r\; \omega_{y}}\end{pmatrix}} \times}}} \\{{{\exp \begin{bmatrix}{{\left( {k - p} \right)\omega_{x}} +} \\\begin{matrix}{{\left( {\omega_{NA} - \omega_{off}} \right)x} +} \\{\left( {l - r} \right)\omega_{y}}\end{matrix}\end{bmatrix}}^{{\iota {({\gamma_{k,l}^{off} - \gamma_{p,r}^{NA}})}}z}} + {c.c.}}\end{matrix} & \lbrack{IV}\rbrack\end{matrix}$

The first three terms in the upper bracket, labeled [I], in equation 8are the result of the off-axis illumination at the edge of the pupil.This image can be measured independently by blocking the extreme offaxis beam and subtracted from the result. The term labeled [II] is thedesired information, the image terms beating against a zero-order beam;because the zero-order beam is not at the correct angle to reset thefrequencies to match the object frequencies (adjusted for magnification)there is a shift between the observed and the actual image planefrequencies {exp[i(ω_(NA)−ω_(off))x]} that will need to be fixedcomputationally (e.g. one is measuring the Fourier components at anintermediate frequency as detailed above). [III] is the dark field fromthe extreme off-axis illumination. Finally the last term, [IV] is thecross-correlated dark field from the two illumination beams.

To remove the unwanted terms in equation 8, five strategies can be used.However, these are not intended to be all-inclusive and otherpossibilities may exist. These are illustrated schematically in FIGS.5A-5E. There are two general approaches, in the FIGS. 5A-5C, thereference beam is added before the object plane. This adds to someadditional complexity in that the off axis and the reference beams giverise to diffracted information and it is necessary to separate out theinformation corresponding to the diffraction from the reference beamfrom the off axis beam. This can be accomplished as shown in the schemeoutlined in FIG. 4. In FIGS. 5D and 5E, the reference beam is addedafter the object plane and before the entrance to the collection lens.In these configurations, the reference beam does not illuminate theobject and hence there is no additional diffraction. This simplifies theanalysis, but at the cost of adding additional optical components in theregion of limited access.

FIG. 5A shows the first embodiment, wherein the third optical system500A can further include a first beamsplitter disposed in the opticalpath of the first optical system to collect a portion of the coherentillumination, one or more optical components to direct the portion ofthe coherent illumination as a reference beam 510′ to illuminate theobject 520 at an angle θ corresponding to less than the entrance angularaperture (<˜sin⁻¹ NA) of the second optical system 5301 and a dynamic(adjustable on/off) physical block 550 disposed in a back pupil plane ofthe second optical system 530 to alternately block and unblock a smallportion of the pupil aperture corresponding to the position of thereference beam 510 in the aperture. One of the advantages of thisembodiment is that all of the information can be retained. However, thisembodiment requires access to the illumination system pupil. In the caseshown in FIG. 5A, the objective pupil has been relayed to an auxiliaryplane where it might be easier to access. The details of this opticalconfiguration will depend on the optical construction of the objectivelens.

FIG. 5B shows the second embodiment 500B, wherein both illuminationbeams can be shifted slightly using a prism 560 so that the zero order209′ can be blocked but there is no change in the exponential factor,only in the transmission factors. Using the first and secondembodiments, one can obtain and subtract dark field from the imageformed by interference of low and high frequencies (the second, fourth,and fifth terms of equation 6). Then one can subtract low frequencyimage without dark field and restore high frequency image by shiftingfrequencies in Fourier space. The second embodiment can be implementedeasily and does not require any access to the objective pupil plane butit has some image-dependent information loss associate with the shiftingof the illumination angles. As shown in FIG. 5B, the prism is located inbetween the object 530 and the entrance aperture of the objective lens530; alternatively it can be located before the object 530. Depending onthe specifics of the object 530, it may be advantageous to dither theposition of only the reference zero-order beam or of both zero-orderbeams.

FIG. 5C shows yet another embodiment using a guided-mode filter(k-vector) 582 to block the zero order transmission just before theobjective 530 and transmit the diffracted information at all otherangles. FIG. 6 shows an exemplary experimental un-optimized k-vectorfilter characteristic of a SiN-on-glass guided mode resonance filter,with a narrow angular width of the coupling. U.S. Pat. No. 5,216,680discloses guided mode resonance filter which can be used as an opticalfilter with very narrow line width and as an efficient optical switch,the disclosure of which is incorporated by reference herein in itsentirety. Referring back to FIG. 5C, it is possible to switch thezero-order on and off by mechanical dithering of the angular position orby dithering by a small degree of rotation around the optical axis. Thiswill allow identification of the source of the diffracted waves in thesub-image. Accordingly, the exemplary third optical system 500C of theapparatus 200 in accordance with various embodiments, can furtherinclude one or more optical components to direct the portion of thecoherent illumination as a reference beam to illuminate the object 530at an angle θ corresponding to less than the entrance angular aperture(<˜sin⁻¹ NA) of said second collection optical system 530, a guided-moderesonance filter (k-vector filter) 582 disposed between the object plane522 and a collection lens of the second optical system 530, and ananother device (not shown) to adjust the position, tilt and rotation ofthe guided-mode resonance filter 582 between positions, tilts androtations in which it alternately transmits and blocks the portion ofthe reference beam transmitted through the object plane.

FIG. 5D shows yet another exemplary third optical system 500D of theapparatus 200 in accordance with various embodiments. The third opticalsystem 500D can further include a first beamsplitter disposed in theoptical path of the first optical system to collect a portion of thecoherent illumination, one or more transfer optics disposed between thefirst optical system and the second optical system, and at least one ofa grating 584 or a grating on a waveguide disposed between the objectplane 522 and a front aperture of the collection lens (objective) of thesecond optical system 530 to reintroduce the portion of the coherentillumination as a reference beam into the second optical system 530 atan angle θ less than the entrance angular aperture (<˜sin⁻¹ NA) of thesecond optical system. In various embodiments, the grating 584 can havea short pitch (high spatial frequency) to avoid diffraction of the wavesincident onto the grating 584 into new directions that are captured bythe objective lens of the second optical system 530. A major advantageof this method is that it does not require switchable gratings ormechanical actuation of the filter, since modulation is by simpleblocking of the incident beam.

FIG. 5E shows the fifth embodiment, wherein the zero order 510′ can bere-injected after the object and just in front of the objective by abeamsplitter 570. Accordingly, the third optical system can include asecond beamsplitter 570 disposed between the object plane 522 and afront aperture of a collection lens (objective) of the second opticalsystem 530 to reintroduce the portion of the coherent illumination as areference beam 510′ into the second optical system 530 at an angle θless than the entrance angular aperture (<˜sin⁻¹ NA) of the secondoptical system 530. The beamsplitter 570 can eliminate all of thediffracted beams associated with the local oscillator, B_(p,r)=0,∀p,r≠0,and simplifies equation 8. The third embodiment does not contain thefirst, second and fifth terms at all, so it is the most robust for theimage processing, but images can be distorted by aberration caused bythe beamsplitter; this aberration can be corrected with additionaloptical components. Using a very thin beamsplitter, e.g., a pellicle,eliminates much of the aberration associated with an expanding beampassing through a tilted thin plate. The use of a beamsplitter impactsthe working distance of the objective, but the depth-of-field andfield-of-view advantages of IIM are retained.

FIGS. 7A and 7B show the frequency space coverage for the structuredillumination approach to IIM shown in FIG. 3 and using the firstembodiment as shown in FIG. 5A. All of the recorded frequencies arewithin the bandpass of the objective lens. The two offset circles 741,742 in FIG. 7A correspond to coverage 740A of both the intermediatefrequency imaging terms and the offset frequency imaging terms beatingwith the intermediate frequency local oscillator. FIG. 7B shows thecoverage 740B after the unwanted dark field and local oscillatorself-imaging terms have been removed and the spatial frequencies havebeen reset to their correct values.

FIGS. 5A and 8B illustrate the frequency space coverage of partialimages with NA of about 0.4 objective. FIG. 8A shows an illustration ofa Manhattan (x, y) geometry pattern 800A used for image resolutionexploration consisting of five nested “ells” and a large box. The linesand spaces of the “ells” are about 240 nm. FIG. 8B shows the intensityFourier space components of the pattern 800A, mapped onto the frequencyspace coverage of the imaging system using a NA=0.4 objective and anillumination wavelength of 633 nm (HeNe laser source). The resolutionlimit of this microscope system with conventional illumination is˜0.6λ/NA (˜950 nm). The two circles at radii of NA/λ (0.41×) and 2NA/λ(0.8/λ) correspond to the approximate frequency space limits forcoherent and incoherent illumination, respectively, and reflect thelow-pass transmission characteristic of the objective lens. The innersets of small shifted circles (radius NA/λ) in FIG. 8B, that extend from−3NA/λ to 3NA/λ (±1.2/λ) in the x- and y-directions, show the frequencyspace coverage added with two offset partial images, one in eachdirection. The imaging is single side-band, only the diffracted planewaves to one side of the object are collected (opposite to the tilt ofthe illumination beam), the square law (intensity) response of the imageformation and detection process restores the conjugate frequency spacecomponents, resulting in the two symmetrically displaced circles in FIG.8B for each partial image. The offset (off-axis tilt) for these imageswas chosen at 2(2π)NA/λ to ensure that there was no overlap between thespectral coverage of the low-frequency partial image (extending out toNA/λ) and the offset images. As discussed previously, improved imagescan be obtained by subtracting the dark-field components of the image(with the zero-order transmission blocked). In the present embodiments,this provided a cosmetic, not a dramatic, improvement to the images.Additional frequency space coverage is available with a second pair ofoff-axis images, represented by the outer sets of shifted circles, witha larger tilt of the illumination plane wave, approaching grazingincidence (limited to 80° by practical considerations such as Fresnelreflectivity in the present experiment). The maximum frequency coveragein these images extends to [sin(80)+NA]/λ=(0.98+NA)/λ=(1.38/λ). Thefrequency-space coverage of the outer circles may be necessary tocapture the fundamental frequency components of the line-space portionof this pattern. There is significant overlap between the frequencycoverage of the first and second set of partial images as illustrated inFIG. 8B. To provide a faithful image, the double coverage of frequencyspace associated with the image spectral overlaps can be excluded. Thiscan be accomplished by filtering the images either optically (withappropriate apertures in the back focal plane) or electronically oncethe images are recorded. Importantly, since each of the partial imagesinvolves only the NA of the objective, this imaging concept retains theworking distance, depth-of-field and field-of-view associated with thelow-NA objective, but has a resolution beyond that achievable with eventhe highest NA objective using traditional illumination approaches.

FIGS. 9A-9F show the preliminary results of an experiment using anNA=0.4 objective with a He—Ne laser illumination (λ=633 nm) and withabout a 240 nm critical dimension structure with correspondingsimulations using the configuration presented in FIG. 5D, blocking thezero-order beam of the reference in the objective lens pupil. FIG. 9A isthe mixed image corresponding to the interference of the low and highimages and FIG. 9B is the corresponding simulation result. FIG. 9C isthe image after subtraction dark field and low frequency image and FIG.9D is the corresponding simulation result. FIG. 9E is restored highfrequency image and FIG. 9F is the corresponding simulated result.

Similarly, results using dynamic (adjustable on/off) physical blockpresented in FIG. 5A are shown in FIG. 10A. The same 260- and 240-nmobjects are imaged as in FIG. 9C; only the final results after the darkfield subtraction, frequency shifting correction and sub-imagecombination are shown. The corresponding cross-cuts are shown in FIG.10B. A total of four offset images, two each in the x- and y-directions,with θ_(ill)=53° and 80° were used along with a 0.4 NA objective. Asdiscussed previously, this configuration provided resolution to <˜240 nmCD. There is overlap in the frequency space coverage between these twoexposures and electronic frequency space filtering is used to assure auniform coverage of frequency space. The present Manhattan geometrystructure has spectral content concentrated along the x- andy-directions, so the offset illuminations were restricted to thosedirections. Adding additional frequency-space coverage for arbitrarilyshaped structures can be accomplished by taking additional sub-imageswith rotation of the object in the (xy) plane. The spatialfrequency-content of the image covers a wide range as a result of thelarge box (at 10× the linewidth of the line:space structures). Thereconstructed image of the same structures obtained by the method withthe beamsplitter configuration presented in FIG. 5E is shown in FIG. 11Aand a crosscut of the image with corresponding simulation is shown inFIG. 11B. The quality of the results for both methods is quitecomparable. The second method retains a long working distance, butrequires access to the imaging system pupil for blocking the zero-order.The first method does not require any modification to the traditionalmicroscopy components, but has reduced working distance due to thebeamsplitter in front of the objective. There are some extra featuresexperimentally as compared to the model due to the lack of precision inmutual phase determination between the sub-images and speckle effectsfrom the coherent illumination. These issues can be reduced by usingimproved arrangements and lower coherence sources. There are otherpossible alternatives; the optimum choice will depend on the specificsof the object and the constraints of specific optical systems.

The embodiments discussed so far provide spatial frequency coverage upto 2π(sin(θ_(ill))+NA)/λ≈2π(1+NA)/λ; that is the maximum illuminationangle offset can be set close to 90° (providing the “1”) and the maximumangle collected by the objective lens corresponds to sin⁻¹(NA). As waspreviously disclosed in relation to the interferometric implementationof IIM, additional spatial frequencies are available by tilting theobject plane relative to the objective lens axis. This allows collectionof spatial frequencies up to 4π/λ, independent of the lens NA. The costis a more complex signal processing requirement since the tilted objectplane results in a nonlinear mapping of spatial frequencies from theobject plane to the laboratory image that must be corrected to achieve agood image. This mapping has been discussed previously. The additionalfrequency space (and hence smaller image features) are available in thestructured illumination embodiments of IIM disclosed herein.

Immersion microscopy is well known to provide higher spatial frequenciesby a factor of the refractive index of the immersion medium, therebyextending the spatial frequency range to as high as 2n/λ. Again theadvantages of immersion are directly applicable to structuredillumination IIM.

Traditionally immersion microscopy has been practiced in reflection witha liquid medium on top of the object, or in transmission where advantageis taken of the high refractive index of the substrate (n_(sub)) as wellas that of a liquid on top of the object. An intermediate possibility isto use just the refractive index of the substrate without an immersionfluid. In this case the spatial frequency range is extended to2π(n_(sub)+NA)λ.

FIG. 12A shows an exemplary apparatus 1200 for microscopy with an IIMarrangement with illumination by evanescent waves extending from asubstrate, according to various embodiments of the present teachings.The apparatus 1200 can include an object plane 1222 on which can bedisposed a first surface of a substrate 1225, wherein the substrate 1225is characterized by a homogeneous refractive index (n_(sub)) and asurface normal 1226. The apparatus 1200 can also include a first opticalsystem disposed to provide an evanescent wave illumination of the objectplane 1222 by providing a substantially coherent illumination of theobject plane 1222, the illumination 1210 characterized by a wavelength λand a radius of curvature and disposed at one of a plurality of incidentwave vectors from about 2π/λ to about 2πn_(sub)/λ with respect to asurface normal of the substrate and at a plurality of azimuth anglesspanning from about 0 to about 2π, wherein the plurality of incidentwave vectors correspond to angles beyond a total internal reflectionangle θ_(c) of the substrate. The apparatus 1200 can also include asecond optical system 1230 disposed to collect portions of theillumination scattered from the object plane 1222, the second opticalsystem 1230 having an optical axis 1236 disposed at one of a pluralityof center wave vectors from about 0 to about 2π/λ with respect to thesubstrate 1225 surface normal and at the azimuth angle corresponding tothe illumination of the first optical system, wherein the second opticalsystem 1230 is characterized by a numerical aperture (NA). FIG. 12Bshows arrangement with tilted optical axis 1236. The apparatus 1200 canalso include a third optical system disposed in an optical path of thefirst optical system to provide interferometric reintroduction of aportion of the coherent illumination (reference beam) into the secondoptical system 1230, wherein each of an amplitude, a phase, a radius ofcurvature and an angle of incidence of the reference is adjusted suchthat a corrected reference wave is present at the image plane of thesecond optical system. The apparatus 1200 can further include anelectronic image device disposed at an image plane of the second opticalsystem that responds linearly to the local optical intensity andtransfers the local optical intensity map across the image plane (asub-image) to a signal processor device in electronic form. Theapparatus 1200 can also include a device for adjusting the first, thesecond, and the third optical systems to collect sub-images fordifferent pairs of the pluralities of incident (first optical system)and collection center (second optical system) wave vectors so as tosequentially obtain a plurality of sub-images corresponding to aplurality of regions of spatial frequency space and an electronic deviceto sequentially receive the electronic form of the sub-images andmanipulate the sub-images to correct for distortions and alterationsintroduced by the optical configuration, store, and combine theplurality of sub-images corresponding to the plurality of regions ofspatial frequency space to create a composite image.

In some embodiments, the third optical system can further include afirst beamsplitter disposed in the optical path of the first opticalsystem before the object to collect a portion of the coherentillumination and one or more optics disposed between the first opticalsystem and the second optical system 1230 to interferometricallyreintroduce the portion of the coherent illumination as a reference beaminto the second optical system 1230 in a position after the exitaperture of a collection (objective) lens, wherein the reintroduction isat one of a position corresponding to a position a zero-order beam wouldhave had if it had been transmitted through a higher NA lens of thesecond optical system 1230 or an aliased position to reduce pixelrequirements of the electronic image device, wherein the signalprocessor is adjusted to compensate for this spatial frequency aliasing(the same concept as the local oscillator frequency introduced earlier).In other embodiments, the third optical system of the apparatus 1200 caninclude one of the configurations shown in FIGS. 5A-5E.

In certain embodiments apparatus 1200 for microscopy with an IIMarrangement with illumination by evanescent waves extending from asubstrate can also include at least one known reference object to covera small part of the image field.

According to various embodiments, there is a method for microscopy byevanescent illumination by illumination through a substrate. The methodcan include providing an object 1220 disposed on a surface of a planarsubstrate 1225 characterized by a homogeneous refractive index (n_(sub))and a surface normal 1226 and providing a first optical system disposedto provide an evanescent wave illumination of the object plane 1222 byproviding a substantially coherent illumination of the object plane1222, the illumination characterized by a wavelength λ and a radius ofcurvature and disposed at one of a plurality of incident wave vectorsfrom about λ to about 2πn_(sub)/λ with respect to a surface normal ofthe substrate and at a multiplicity of azimuth angles spanning 0 to 2π,wherein the plurality of incident wave vectors correspond to anglesbeyond a total internal reflection angle θ_(c) of the substrate. Themethod can further include providing a second optical system 1230 havingan optical axis 1136 disposed at one of a plurality of center wavevectors from about 0 to about 2π/λ with respect to the surface normal,wherein the second optical system 1230 is characterized by a numericalaperture (NA). The method can also include providing a third opticalsystem disposed in an optical path of the first optical system toprovide interferometric reintroduction of a portion of the coherentplane wave illumination (reference beam) into the second optical system1230, wherein the amplitude, phase, and position of the reintroducedillumination plane wave in the back focal plane of the second opticalsystem 1230 can be adjusted. The method can further include recording asub-image of the object 1220 at an object plane 1222 using an electronicimage device, wherein the sub-image is formed as a result ofinterference of the coherent plane wave illumination of the object andthe reference beam; adjusting the first, the second, and the thirdoptical systems to sequentially collect a plurality of sub-imagescorresponding to a plurality of regions of spatial frequency space;manipulating each of the plurality of sub-images using a signalprocessor to correct for distortions and alterations introduced by theoptical configuration; and combining the plurality of sub-images into acomposite image to provide a substantially faithful image of the object.In various embodiments, the method can further include one or moreprocesses of subtraction of dark field images, subtraction of backgroundimages, shifting of spatial frequencies in accordance with the opticalconfiguration, and elimination of one or more overlapping coverages ofthe frequency space wherein the elimination operations can be performedeither in the optical systems or in the signal processing. In someembodiments, the method can also include selection of the regions ofspatial frequency space to provide a more or less faithful image of theobject in the object plane. Neumann et al. in Optics Express, Vol. 16,No. 25, 2008 pp 20477-20483 describes an evanescent wave illuminationfor further extending the resolution limit of imaging interferometricmicroscopy to λ\2(n+1), the disclosure of which is incorporated hereinby reference in its entirety.

In various embodiments, the step of providing an object 1220 disposed ona surface of a planar substrate 1225 can include providing a claddinglayer surrounding the object 1220 and the object 1220 disposed over thesubstrate 1225. The extent of excitation region due to evanescent waveillumination, normal to the interface is given by an exponential decayfunction with a 1/e length of λ/2π√{square root over (n_(sub) ² sin²θ−n_(clad) ²)}, where n_(sub) is the refractive index of the substrateand n_(clad) is the refractive index of the superstrate or claddingmaterial surrounding the object 1220. The spatial localization canprovide benefit, for example in TIRF (total internal reflectionfluorescence) the localization is much larger than can be achieved witha simple focus or even with confocal microscopy. In other cases, thisdecay length can be a restriction, for example, in lithography studieswhere there might be multiple layers of material (bottom AR coating andphotoresist for example) and the structural variation between theselayers is of interest. Hence, the addition of a cladding layersurrounding the object can allow some degree of tuning of the decaylength, and thereby control the signal to noise ratio.

FIGS. 13A-13C shows several exemplary techniques to illuminate throughthe substrate 1325. FIG. 13A shows coupling of incident beam 1310through a side 1327 of the substrate 1325, which can be polished at anangle different from normal to the object 1320; in other words thesubstrate 1325 can be a prism. FIG. 13B shows one or more gratings 1364on a side of the substrate 1325 the same as that where the object 1320can be located. Alternatively, the gratings 1364 can be placed on a sideopposite to that of the object 1320. FIG. 13C shows coupling of theincident beam 1310 using one or more prisms 1362.

FIG. 14A shows a Manhattan (x-, y-geometry) test pattern, scaled todifferent dimensions. The Fourier intensity transform of this patternfor a linewidth (critical dimension or CD) of 180 nm is shown in FIG.14B and for a CD of 150 nm in FIG. 13C. The circles in FIGS. 14B and 14Ccorrespond to the bandpass limits of various microscopy configurations.The circle in the center of FIG. 14B, with a radius of NA/λ=0.4/λ,corresponds to the Abbé-limit spatial frequency range captured withon-axis coherent illumination (NA_(ill)=0). The inner set of shiftedcircles in FIG. 14B (only single sidebands are shown for clarity; thecomplex conjugate regions are covered as well) correspond to IIM withoff-axis illumination beams at θ_(ill)=53° in the x, y-directions thatextend the frequency coverage to a radius 3NA/λ˜1.2/λ. Additionalfrequency space coverage (second pair of circles) is available usingevanescent wave illumination extending the frequency space coverage to aradius of (n_(sub) sin θ_(ill)+NA)/λ˜1.87/λ (with θ_(ill)=76°) withouttilt of the microscope optical axis. The frequency space coverage alongwith the corresponding structure Fourier intensity plot for thestructure with CD=150 nm is shown in FIG. 14C. The third pair ofoff-axis sub-images in FIG. 14C correspond to the tilted optical axis.This frequency region is elliptical rather than circular, due tononparaxial and conical diffraction effects associated with the off-axisoptical system.

FIG. 15A shows the experimental result for an object containing both180- and 170-nm CD structures in a single large-field image using theapparatus of FIG. 12A (two pairs of offset illumination, one at 53° inair and one at 76° in the substrate and collection with the optical axisalong the substrate's surface normal as shown in FIG. 12A. The 180-nm CDobject is within the bandwidth capabilities of this optical system whilethe 170-nm CD object has significant spatial frequencies that extendbeyond the optical system bandwidth and so is not fully resolved. Thefive nested “ell” shapes are distinguishable for the 180-nm CD, but notfor the 170-nm CD. The positions of the two objects are correctlyrestored by the image restoration procedure as is evident from the goodpositional overlap between the experimental and theoretical cross-cutsin FIG. 15B.

FIG. 16A shows reconstructed high frequency image of a 150 nm structureusing evanescent illumination and a tilted optical system, shown in FIG.12B, with the highest spatial frequencies collected with the opticalaxis tilted with respect to the substrate's surface normal. FIG. 16Bshows high frequency image simulation of a 150 nm structure usingevanescent illumination and a tilted optical system, shown in FIG. 12B.FIG. 16C shows experimental and simulation cross-cuts of images shown inFIGS. 16A and 16B. FIG. 16D shows reconstructed composite image of a 150nm structure using evanescent illumination and a tilted optical system,shown in FIG. 12B. FIG. 16E shows composite image simulation of a 150 nmstructure using evanescent illumination and a tilted optical system,shown in FIG. 12B. FIG. 16F shows experimental and simulation cross-cutsof images shown in FIGS. 16D and 16E.

Evanescent illumination can be combined with structural illuminationeliminating the need for access to the back focal plane. This moves theinterferometer to the front of the objective lens and makes IIM readilyadaptable to existing microscopes. Structural illumination is roughlyequivalent to recording the spectral information at an intermediatefrequency; additional computation is required to reset the frequencies.But this frequency shifting can reduce the camera pixel size and countrequirements. Evanescent wave illumination can be used to extend theresolution of IIM to λ/2(n+1). Furthermore, IIM provides an importantadvantage over conventional immersion microscopy techniques. Since onlya relatively small region of frequency space (˜NA/λ) is recorded in eachsub-image, the aberration requirements on the objective lens aredramatically reduced. Hence, a simple set of prisms or gratings can beused to extract, and conventional air-based lenses to capture, theinformation. As is always the case, there is a trade-off between thenumber of sub-images and the NA of the objective lens.

FIG. 17 shows the possible increase of NA_(eff), drawn for a 0.4 NAsystem. As the frequency coverage is extended, the use of higher NAlenses can reduce the number of sub-images required for a more completecoverage of frequency space. Of course the required coverage isdependent on the pattern, and there are some applications, for examplein metrology for integrated circuits, where coverage of a subset of thefull frequency space is appropriate, where the range of spatialfrequencies in the object are limited by lithographic consideration.

There are diffracted beams corresponding to even larger spatialfrequencies (smaller features) scattered back into the substrate atangles larger than the critical angle. For planar substrate, these beamsare totally internally reflected and are not accessible. FIG. 18 showsanother exemplary IIM optical arrangement for an apparatus 1800 formicroscopy that provides access to the higher spatial frequency termsand thereby provides higher resolution, according to various embodimentsof the present teachings. The apparatus 1800 can include an object plane1822 on which can be disposed a first surface over a planar substrate1825, wherein the substrate 1825 is characterized by a homogeneousrefractive index (n_(sub)) and a surface normal 1826. The apparatus 1800can also include a first optical system disposed to provide asubstantially coherent illumination of the object plane, theillumination characterized by a wavelength λ and a radius of curvatureand disposed at one of a plurality of incident wave vectors from about 0to about 2πn_(sub)/λ with respect to a surface normal 1822 of thesubstrate 1825 and at a plurality of azimuth angles spanning from about0 to about 2π. The apparatus 1800 can further include at least onegrating 1864 on the side of the substrate 1825 opposite the object plane1822, wherein each grating 1864 is characterized by a period, a depth, agrating profile, a position, and an extent to further scatter reflectedwaves resulting from the coherent illumination of the object plane intopropagating waves in the medium below the substrate. In someembodiments, the medium below the substrate 1825 can be air. In otherembodiments, the medium can be a vacuum. However, the medium can includeany other suitable material. The apparatus 1800 can further include asecond optical system 1830 having an optical axis 1836 disposed at oneof a plurality of center wave vectors from about 0 to about 2π/λ withrespect to the surface normal 1826, wherein the second optical system1830 can include one or more gratings 1864 on the second side of thesubstrate 1825 and is characterized by a numerical aperture (NA). Theapparatus 1800 can also include a third optical system disposed in anoptical path of the first optical system to provide interferometricreintroduction of a portion of the coherent illumination (referencebeam) into the second optical system 1830, wherein each of an amplitude,a phase, a radius of curvature and an angle of incidence of thereference can be adjusted such that a corrected reference wave ispresent at the image plane of the second optical system. The apparatus1800 can further include an electronic image device disposed at an imageplane of the second optical system 1830 that responds linearly to thelocal optical intensity and transfers the local optical intensity mapacross the image plane (a sub-image) to a signal processor device inelectronic form, a signal processor that receives the electronic form ofthe sub-image and manipulates the sub-image to correct for distortionsand alteration introduced by the optical configuration, and anelectronic device to sequentially collect, store and combine a pluralityof sub-images corresponding to a plurality of regions of spatialfrequency space to create a composite image, wherein the plurality ofsub-images are formed as a result of adjustments to the first, thesecond, and the third optical systems. In various embodiments, the thirdoptical system of the apparatus 1800 can include one of the thirdoptical system configurations shown in FIGS. 5A-5E.

In various embodiments, the grating 1864 profile can have an impact onthe extraction efficiency. In some embodiments, the grating 1864 canhave a sinusoidal profile. A sinusoidal grating has components in itsFourier transform only at ±1/d. In other embodiments, the grating 1864can have a rectangular profile. A rectangular grating has many moreFourier components that can lead to coupling of additional scatteredimage plane waves across the interface. For equal line: space grating,the second order Fourier coefficient (@±2/d) vanishes, although forsufficiently deep gratings, comparable to the wavelength, additionalcoupling terms can arise. The third order terms (at ±3/d) are alwayspresent for rectangular grating profiles. This can give rise to multiplecoupling orders which can lead to artifacts in the sub-images. In somearrangements, this is not an issue because of the spatial separation ofthe scattered spatial frequency information at the bottom of thesubstrate (as can be seen in FIG. 18). In this case, the bottomsubstrate plane is separated from the object plane and the differentspatial frequency components, propagating at different angles, haveseparated to some extent by the time they reach this plane. If thethickness of the substrate 1825 is significantly larger than the fieldof view (illuminated aperture at the image plane), this separation canbe large enough to avoid issues associated with higher order coupling atthe bottom surface extraction grating. Thus, there is engineeringtrade-off in choosing the thickness of the substrate 1825, theseparation is better if it is thicker, but the phase distortions areincreased.

Alternative collection schemes can include using one or more prisms1974, as shown in FIG. 19. In some embodiments, the prism 1974 can befabricated as part of the substrate 1925. In other embodiments, indexmatching fluid 1972 can be used.

In certain embodiments apparatus 1800 for microscopy can also include atleast one known reference object to cover a small part of the imagefield.

According to various embodiments, there is a method for microscopy byillumination through a substrate. The method can include providing anobject 1820 disposed over a first side of a planar substrate 1825, thesubstrate characterized by a homogeneous refractive index (n_(sub)) anda surface normal 1826 such that the object 1820 is separated from thesubstrate 1825 by a distance of no more than about ≦λ. The method canalso include providing at least one grating 1864 on the side of thesubstrate 1825 opposite the object plane 1822, each grating 1864characterized by a position, a period, a depth, and a grating profile,wherein each of the gratings 1864 can further scatter reflected wavesresulting from the coherent illumination of the object into propagatingwaves in the medium below the substrate. The method can further includeproviding a first optical system disposed to provide a substantiallycoherent illumination of the object plane, the illuminationcharacterized by a wavelength λ and a radius of curvature and disposedat one of a plurality of incident wave vectors from about 0 to about2πn_(sub)/λ with respect to a surface normal of the substrate and at aplurality of azimuth angles spanning from about 0 to about 2π. Themethod can also include providing a second optical system 1830 having anoptical axis 1836 disposed at one of a plurality of center wave vectorsfrom about 0 to about 2π/λ with respect to the surface normal 1826,wherein the second optical system 1830 includes at least one grating1864 on the second side of the substrate 1825 and is characterized by anumerical aperture (NA). The method can further include providing athird optical system disposed in an optical path of the first opticalsystem to provide interferometric reintroduction of a portion of thecoherent illumination (reference beam) into the second optical system1830, wherein each of an amplitude, a phase, a radius of curvature andan angle of incidence of the reference is adjusted as required such thata corrected reference wave is present at the image plane of the secondoptical system 1830. The method can also include providing an electronicimage device disposed at an image plane of the second optical system1830 that responds linearly to the local optical intensity and transfersthe local optical intensity map across the image plane (a sub-image) toa signal processor device in electronic form, providing a signalprocessor that receives the electronic form of the sub-image,manipulating each of the plurality of sub-images using the signalprocessor to correct for distortions and alterations introduced by theoptical configuration, and combining the plurality of sub-images into acomposite image to provide a substantially faithful image of the object.In various embodiments, the method can further include one or moreprocesses of subtraction of dark field images, subtraction of backgroundimages, shifting of spatial frequencies in accordance with the opticalconfiguration, and elimination of one or more overlapping coverages ofthe frequency space wherein the elimination operations can be performedeither in the optical systems or in the signal processing. In someembodiments, the method can also include selecting regions of spatialfrequency space to provide a more or less faithful image of the objectin the object plane.

For various IIM configurations shown in FIGS. 3, 12, and 18, thecoherence length>>sample (object) dimensions. The He—Ne laser has a longcoherence length of many cm, and this makes the experimental arrangementsimpler, as it is not necessary to critically match the interferometerlengths between the objective arm and the zero-order reinjection arm.However, it does increase spurious speckle effects associated with straylight and multiple reflections from various optical surfaces in thesetup. These effects can be mitigated by choosing a source withsufficient coherence for the IIM measurements, but insufficientcoherence for Fabry-Perot effects, e.g. between the front and back sidesof the substrate or between the substrate and the objective entrancesurface. Since, these dimensions are very different, μm scale for thesample to several mm for the substrate thickness and substrate-objectivedistance, it is possible to minimize unrelated Fabry-Perot effects whileretaining all of the resolution of IIM.

Tiling of Frequency Space

In general, the spatial frequency location of the informationcorresponding to a specific angle of illumination (includingillumination through the substrate) and angle of collection (θ)corresponds to

${\overset{\rightarrow}{k}}_{scatter} = {{\frac{2\; {\pi (n)}}{\lambda}\sin \; \theta_{illumination}{\hat{e}}_{illumination}} - {\frac{2\; \pi \; n_{sub}}{\lambda}\sin \; \theta_{scattered}{\hat{e}}_{scattered}}}$

In the above equation, (n) in the first term is adjusted as appropriate,for example, for illumination in air, n=1 while for illumination(evanescent) through a substrate, n=n_(sub)=1.5 for glass. In keepingwith the notation established above, θ_(scattered) is the angle in thesubstrate and so the factor n_(sub) is appropriate; a grating can beused to shift the spatial frequencies into the air propagation bandpassas necessary.

Both angles as well as the pitch of any gratings can provide someflexibility in the tiling of frequency space, i.e. in choosing theregions of frequency images into a complete image. The maximum spatialfrequency, k_(max)=2πf_(max)=2π(2n_(sub)/λ) is obtained when both anglesare close to 90°. Since we can resolve a half pitch, this leads to anAbbe resolution limit of λ/4n_(sub). The optimum strategy is patterndependent, for example, for Manhattan geometry structures with edgesconfined to a rectangular grid, often found in integrated circuits, itis important to capture the frequency information along the axes and ofless consequence to capture the information away from the axes where theFourier transform of the pattern has lower spectral intensity. In theexamples shown in FIGS. 19A and 19B, only one principal axis isconsidered, but the generalization to complete coverage isstraightforward.

FIGS. 20A and 20B show two alternate embodiments for providing coveragefrom f_(x)=0 to f_(x)=2n_(sub)/λ with a fixed objective NA. Thefrequency space coverages shown in FIGS. 20A and 20B are designed for amaximum spatial frequency of 3/λ (2n_(sub)/λ), and an objective of NA of0.65. In FIG. 20A, a minimum number of subimages are used. The centralsmall circle corresponds to conventional, normal incidence coherentillumination with the radius of the circle being about 0.65/λ. The nextsub-image is taken with off-axis illumination through the substrate atan angle of about 53°; this corresponds to effective NA_(ill) of about1.2. The scattered light can be detected either from the top (throughair) or through the substrate, the collection geometry can be similar tothat shown in FIG. 18, except for the illumination direction. Azero-order (interferometric reference) beam can be used in IIM toprovide access to the essential phase information as well as to allowunambiguous assignment of the directly measured spatial frequencies. Thesquare law, intensity detection process restores both the complexconjugate frequencies within the symmetrically located dotted circle inthe figure. A third sub-image can be taken with grazing incidenceillumination through the substrate, and with higher scattered spatialfrequencies with the use of a grating of period λ/0.8 for extraction asin FIG. 18. Again, the complex conjugate spatial frequencies arerestored by the square-law detection process. For a Manhattan geometryobject, a similar set of sub-images in the orthogonal direction can beused, for a total of five sub-images; arbitrary structures may requireadditional sub-images to fill all of frequency space.

FIG. 20B shows a second tiling embodiment, using four sub-images, butprovides more robust coverage of frequency space (fewer missed spatialfrequencies in the regions where the circles abut). The central circleis the same as in the previous example, illumination at normal incidenceand collection with a conventional 0.65 NA optical system. The secondinnermost set of circles corresponds to illumination at grazingincidence in air (NA_(ill)˜1). The next innermost set corresponds to thesame illumination condition, but to collection through a glasssubstrate. The final outermost set of circles corresponds toillumination at grazing incidence through the substrate and collectionwith the same grating to allow high spatial frequencies (collection oflight scatted at angles beyond the critical angle in the glass). Thedisclosed exemplary embodiments provide an example of the flexibilityoffered by the IIM process. The choice of tiling strategy will depend onthe object to be imaged. In general, it is best not to put a collectionboundary in a region of high spectral intensity to minimize Gibbs effectoscillations of the observed sub-image structure. In addition, thestrength of scattered spatial frequency components in the regionsbetween the circles will be a factor in selecting an IIM tilingstrategy.

It should be noted that the tiling with circular regions is not arequirement, but is convenient as a result of the symmetry of opticallenses. In some cases, a square aperture, which can be provided eitheroptically or electronically during the subimage manipulations, can proveadvantageous. In particular, a square aperture can be configured toprovide more robust coverage at the boundaries between sub-images (e.g.two squares can match along the line, while two circles can only touchat a point). The tilings in FIG. 19B show some overlap regions. Severalstrategies are available for dealing with the multiple counting infrequency space that these overlaps imply. The simplest is just toremove the double counting in the computation of the sub-imagecombination. Alternatively, a graded transfer function can be applied inthe region of the overlap to minimize artifacts from imperfectcancellation of Gibbs effect oscillations in the two sub-images. Thesimplest approach is to calculate the Fourier transform of thesub-image, apply appropriate filters and inverse transform back to realspace. The apparatus of image signal processing is very rich, and manyof its techniques can be applied to this image reconstruction problem.

For arbitrary images, where a-priori information on likely orientationsand spatial frequency content is not available, for example biologicalspecimens, additional sub-images can be used in order to get a morecomplete coverage of spatial frequency space. An example of coveringmost of spatial frequency space is given in FIG. 21. This consists of 13sub-images: the two off-axis sub-images shown in the top of FIG. 20A arerepeated with rotation angles of 45°, 90° and 135° (there is no need torepeat the low-frequency sub-image) for a total of 9 sub-images;additional high frequency subimages at rotation angles of 22.5°, 67.5°,11 2.5°, and 157.5°, for a total of 13 subimages, complete the coverageexcept for small regions near the outer periphery of frequency space. Itshould be noted that there are only three optical configurations;on-axis illumination (low frequency), middle frequency, and highfrequency, the remaining sub-images are obtained by a simple samplerotation. Furthermore, provision can be made for illumination throughthe substrate for the middle and high frequency coverage as the sampleis rotated.

The number of sub-images can be reduced by increasing the objective NA.As can be seen in FIG. 22, the number of sub-images for nearly fullcoverage is reduced to 5 for a NA=0.95, corresponding to a very high NAair-based objective. The specifics of the arrangement is that the lowfrequency sub-image is taken for normal incidence (NA_(ill)=0); each ofthe offset sub-images is at NA_(ill)+G/λ=2 which can be achieved withgrazing incidence illumination through the substrate along with agrating with a period of λ/0.5.

FIG. 23 provides two similar 1D tiling strategies for a siliconsubstrate (n_(sub)=3.6 at 1064 nm), one (vertical) for a 0.65 NA andanother (horizontal) for a 1.4 NA conventional immersion objective. Asmany as seven sub-images may be used to provide a complete coveragealong just one axis for the 0.65 NA, whereas only three are sufficientfor the large NA. The area of frequency space, and the required numberof sub-images for nearly complete coverage, increases as n². Scalingfrom FIG. 20A suggests that as many as (3.6/1.5)²×13˜75 sub-images wouldbe required for full coverage with the 0.64 NA objective. This suggeststhat there will be great advantage in knowing something about the imageand its spectral content. One situation where this is clearly possibleis in the inspection of silicon integrated circuits. The demands ofmanufacturable lithography at the nanoscale are forcing lithographers torestrict the range of patterns allowed in modern integrated circuits.This is often referred to as lithography “friendly” design, which ingeneral is forcing the patterns closer to periodic grating patterns. Inturn, a lithography “friendly” circuit is a microscopy “friendly”circuit with a limited range of spatial frequencies, hence completecoverage of spatial frequency space is not required to reconstruct animage. Immersion lenses are not available at an NA corresponding to therefractive index of silicon (3.6). An available immersion lens designedfor more modest NAs of ˜1.4 can be used with the addition of gratings tocouple the higher spatial frequency light out of the substrate. An issuewith the very high NA immersion lens is that these lenses typically havea very short working distance, which in turn will require a very thinsubstrate, or a specially designed objective.

Imaging interferometric microscopy techniques as described above aresensitive to the optical refractive index variation of the objectmaterials and does not contain any material specific information.Imaging interferometric microscopy can be applied to get material andchemical information using coherent anti-Stokes Raman scattering (CARS)spectroscopic microscopy. An apparatus for coherent anti-Stokes Raman(CARS) microscopy can include any suitable optical arrangement as shownin FIGS. 1, 3, 5A-5E, 12A, 12B 13A-13C, 18, and 19. In particular, theapparatus for CARS microscopy can include an object plane 122, 222,1222, 1822 on which can be disposed a first surface of a planarsubstrate 125, 225, 1225, 1825, wherein the substrate 125, 225, 1225,1825 can be characterized by a homogeneous refractive index (n_(sub))and a surface normal 226, 1226, 1826. The apparatus for CARS microscopycan also include a first optical system disposed to provide aillumination of the object plane 122, 222, 1222, 1822, the illuminationcharacterized by two substantially coincident coherent beams 110, 110′,210, 210′, with wavelengths λ₁ and λ₂ and corresponding angularfrequencies ω₁ and ω₂ with ω₁>ω₂, a radius of curvature, and disposed atone of a plurality of incident wave vectors from about 0 to about2πn_(sub)/λ₁ with respect to a surface normal of the substrate 125, 225,1225, 1825 and at a multiplicity of azimuth angles spanning 0 to 2π. Theapparatus for CARS microscopy can also include a second optical system(collection) 130, 230, 530, 1230, 1830 having an optical axis 136, 236,536, 1236, 1836 disposed at one of a plurality of center wave vectorsfrom about 0 to about 2πn_(sub)/λ₁ with respect to the surface normal,wherein the second optical system 130, 230, 530, 1230, 1830 ischaracterized by a numerical aperture (NA) and is responsive primarilyto optical signals at frequencies greater than ω₁. The apparatus forCARS microscopy can further include a third optical system disposed inan optical path of the first optical system to provide interferometricreintroduction of a reference illumination (reference beam) at afrequency of 2ω₁−ω₂, into the second optical system 130, 230, 530, 1230,1830, wherein each of an amplitude, a phase, a radius of curvature andan angle of incidence of the reference is adjusted as required such thata corrected reference wave is present at the image plane of the secondoptical system 130, 230, 530, 1230, 1830. The apparatus for CARSmicroscopy can also include an electronic image device disposed at animage plane 124, 224 of the second optical system 130, 230, 530, 1230,1830 that responds linearly to the local optical intensity and transfersthe local optical intensity map across the image plane (a sub-image) toa signal processor device in electronic form, a signal processor thatreceives the electronic form of the subimage and manipulates thesub-image to correct for distortions and alteration introduced by theoptical configuration, and an electronic device to sequentially collect,store and combine a plurality of sub-images corresponding to a pluralityof regions of spatial frequency space to create a composite image,wherein the plurality of sub-images are formed as a result ofadjustments to the first, the second, and the third optical systems.

In various embodiments, the third optical system of the apparatus forCARS microscopy can include a first beamsplitter disposed in the opticalpath of the first optical system before the object plane 122, 222, 1222,1822 to collect a portion of the coherent illumination and one or moreoptics disposed between the first optical system and the second opticalsystem 130, 230, 530, 1230, 1830, wherein the optics includes anonresonant nonlinear material configured to generate the anti-Stokesfour-wave mixing frequency 2ω₁−ω₂ and exclude the fundamentalfrequencies (ω₁ and ω₂), and to interferometrically reintroduce theportion of the anti-Stokes coherent illumination as a reference beaminto the second optical system 130, 230, 530, 1230, 1830 in a positionafter the exit aperture of a collection (objective) lens, wherein thereintroduction is at one of a position corresponding to a position azero-order beam would have had if it had been transmitted through anappropriate higher NA lens of the second optical system 130, 230, 530,1230, 1830 as shown in FIG. 1 or an aliased position to reduce pixelrequirements of the electronic image device, wherein the signalprocessor is adjusted to compensate for this spatial frequency aliasing.

In various embodiments, the third optical system of the apparatus forCARS microscopy can include one of the third optical systemconfigurations shown in FIGS. 5A-5E. In some embodiments, the apparatusfor CARS microscopy can include a third optical system 500E in aconfiguration shown in FIG. 5E. The third optical system can include afirst beamsplitter disposed in the optical path of the first opticalsystem before the object plane 522 to collect a portion of the coherentillumination one or more transfer optics disposed between the firstoptical system and the second optical system 530, wherein the opticsincludes a nonresonant nonlinear material 520 configured to generate theanti-Stokes four-wave mixing frequency 2ω₁−ω₂ and exclude thefundamental frequencies (ω₁ and ω₂), and a second beamsplitter 570disposed between the object plane 522 and a front aperture of acollection lens (objective) of the second optical system 530 toreintroduce the portion of the anti-Stokes coherent wave illumination asa reference beam 510′ into the second optical system 530 at an angle θless than the entrance angular aperture (<˜sin⁻¹ NA) of the secondoptical system 530.

In other embodiments, the apparatus for CARS microscopy can include athird optical system 500D in a configuration shown in FIG. 5D. The thirdoptical system 500D can further include a first beamsplitter disposed inthe optical path of the first optical system to collect a portion of thecoherent illumination, one or more transfer optics disposed between thefirst optical system and the second optical system, wherein the opticsincludes a nonresonant nonlinear material configured to generate theanti-Stokes four-wave mixing frequency 2ω₁−ω₂ and exclude thefundamental frequencies (ω₁ and ω₂). The third optical system 500D canalso include at least one of a grating 584 or a grating on a waveguidedisposed between the object plane 522 and a front aperture of thecollection lens (objective) of the second optical system 530 toreintroduce the portion of the anti-Stokes coherent wave illumination asa reference beam 510′ into the second optical system 530 at an angle θless than the entrance angular aperture (<˜sin⁻¹ NA) of the secondoptical system 530.

In other embodiments, the apparatus for CARS microscopy can include athird optical system 500A in a configuration shown in FIG. 5A. The thirdoptical system 500A can further include a first beamsplitter disposed inthe optical path of the first optical system to collect a portion of thecoherent illumination, one or more transfer optics, wherein the one ormore optics can include a nonresonant nonlinear material configured togenerate the anti-Stokes four-wave mixing frequency 2ω₁−ω₂ and excludethe fundamental frequencies (ω₁ and ω₂) and wherein at least one of theone or more optics is disposed to direct the portion of the anti-Stokescoherent plane wave illumination as a reference beam to illuminate theobject at an angle θ corresponding to less than the entrance angularaperture (<˜sin⁻¹ NA) of the second optical system 530. The thirdoptical system 500A can also include a dynamic (on/off) physical block550 disposed in a back pupil plane of the second optical system 530 toalternately block and unblock a small portion of the pupil aperturecorresponding to the position of the reference beam 510′ in theaperture.

In various embodiments, the apparatus for CARS microscopy can include athird optical system 500C in a configuration shown in FIG. 5C. The thirdoptical system 500C can further include a first beamsplitter disposed inthe optical path of the first optical system to collect a portion of thecoherent illumination, one or more transfer optics, wherein the one ormore optics can include a nonresonant nonlinear material configured togenerate the anti-Stokes four-wave mixing frequency 2ω₁−ω₂ and excludethe fundamental frequencies (ω₁ and ω₂) and wherein at least one of theone or more optics is disposed to direct the portion of the anti-Stokescoherent plane wave illumination as a reference beam to illuminate theobject at an angle θ corresponding to less than the entrance angularaperture (<˜sin⁻¹ NA) of the second optical system 530. The thirdoptical system 500C can also include a guided-mode resonance filter(k-vector filter) 582 disposed between the object plane 522 and acollection lens of the second optical system 530 and an another device(not shown) to adjust the position, tilt and rotation of the guided-moderesonance filter 582 between positions, tilts and rotations in which italternately transmits and blocks the portion of the reference beamtransmitted through the object plane.

In certain embodiments, the apparatus for CARS microscopy can alsoinclude at least one known reference object to cover a small part of theimage field. In some embodiments, the first, the second, and the thirdoptical systems can be arranged in a transmission configuration.

In other embodiments, the first, the second, and the third opticalsystems can be arranged in a reflection configuration. In someembodiments, the plurality of incident wave vectors of the first opticalsystem can include wave vectors less than about 2π/λ₁ wherein these wavevectors are accessed by illumination of the substrate at polar anglesbetween 0 and π/2. In other embodiments, the plurality of incident wavevectors of the first optical system can include wave vectors betweenabout 2π/λ₁ and about 2πn_(sub)/λ₁, wherein these wave vectors areaccessed by evanescent wave illumination of the object through thesubstrate. Furthermore, the apparatus for CARS microscopy can use any ofthe arrangements shown in FIGS. 13A-13C for coupling light into thesubstrate for illumination through the substrate 125, 225, 1225, and1825.

In some other embodiments, the plurality of center wave vectors of thesecond optical system 130, 230, 530, 1230, 1830 can include only centerwave vectors less than about 2π/λ, wherein these center wave vectors areaccessed by an optical system above the object plane of the substrate125, 225, 1225, 1825. In certain embodiments, the plurality of centerwave vectors of the second optical system 130, 230, 530, 1230, 1830 caninclude center wave vectors between 2π/λ₁ and 2πn_(sub)/λ₁, wherein thecenter wave vectors greater than 2π/λ₁ are accessed through thesubstrate 1251 225, 1225, 1825 and the second optical system 130, 230,5301 1230, 1830 can include one or more gratings on the side of theplanar substrate 125, 225, 1225, 1825 opposite the object plane 122,222, 1222, 1822, wherein each grating is characterized by a position, apitch, and a grating profile.

According to various embodiments, there is a method for coherentanti-Stokes Raman (CARS) microscopy. The method for CARS microscopy caninclude providing an object 120, 220, 1220, 1820 disposed over a planarsubstrate 125, 225, 1225, 1825, wherein the substrate 125, 225, 122511825 is characterized by a homogeneous refractive index (n_(sub)) and asurface normal and providing a first optical system disposed to providea illumination of the object plane 122, 222, 1222, 1822, theillumination characterized by two substantially coincident coherentbeams with wavelengths λ₁ and λ₂ and corresponding angular frequenciesω₁ and ω₂ with ω₁>ω₂, a radius of curvature, and disposed at one of aplurality of incident wave vectors from about 0 to about 2πn_(sub)/λ₁with respect to a surface normal 126, 226, 1226, 1826 of the substrate125, 225, 1225, 1825 and at a multiplicity of azimuth angles spanning 0to 2π. The method can also include providing a second optical system(collection) 130, 230, 1230, 1830 having an optical axis 136, 236, 1236,1836 disposed at one of a plurality of center wave vectors from about 0to about 2πnsub/λ₁ with respect to the surface normal 125, 225, 1225,1825, wherein the second optical system 130, 230, 1230, 1830 ischaracterized by a numerical aperture (NA) and is responsive primarilyto optical signals at frequencies greater than ω₁ and providing a thirdoptical system disposed in an optical path of the first optical systemto provide interferometric reintroduction of a reference illumination(reference beam) at a frequency of 2ω₁−ω₂, into the second opticalsystem 130, 230, 1230, 1830, wherein each of an amplitude, a phase, aradius of curvature and an angle of incidence of the reference isadjusted as required such that a corrected reference wave is present atthe image plane of the second optical system 130, 230, 1230, 1830. Themethod can further include providing an electronic image device disposedat an image plane of the second optical system 130, 230, 1230, 1830 thatresponds linearly to the local optical intensity and transfers the localoptical intensity map across the image plane (a sub-image) to a signalprocessor device in electronic form, providing a signal processor thatreceives the electronic form of the sub-image, manipulating thesub-image using the signal processor to correct for distortions andalteration introduced by the optical configuration, providing anelectronic device to sequentially collect, store and combine a pluralityof sub-images corresponding to a plurality of regions of spatialfrequency space to create a composite image, wherein the plurality ofsub-images are formed as a result of adjustments to the first, thesecond, and the third optical systems, and combining the plurality ofsub-images into a composite image to provide a substantially faithfulimage of the object 120, 220, 1220, 1820.

According to various embodiments, the method can further include one ormore processes of subtraction of dark field images, subtraction ofbackground images, shifting of spatial frequencies in accordance withthe optical configuration, and elimination of one or more overlappingcoverages of the frequency space wherein the elimination operations canbe performed either in the optical systems or in the signal processing.In some embodiments, the method can further include selecting regions ofspatial frequency space to provide a more or less faithful image of theobject 120, 220, 1220, 1820 in the object plane 122, 222, 1222, 1822.

While the invention has been illustrated with respect to one or moreimplementations, alterations and/or modifications can be made to theillustrated examples without departing from the spirit and scope of theappended claims. In addition, while a particular feature of theinvention may have been disclosed with respect to only one of severalimplementations, such feature may be combined with one or more otherfeatures of the other implementations as may be desired and advantageousfor any given or particular function. Furthermore, to the extent thatthe terms “including”, “includes”, “having”, “has”, “with”, or variantsthereof are used in either the detailed description and the claims, suchterms are intended to be inclusive in a manner similar to the term“comprising.” As used herein, the term “one or more of” with respect toa listing of items such as, for example, A and B, means A alone, Balone, or A and B.

Other embodiments of the invention will be apparent to those skilled inthe art from consideration of the specification and practice of theinvention disclosed herein. It is intended that the specification andexamples be considered as exemplary only, with a true scope and spiritof the invention being indicated by the following claims.

1. An apparatus for microscopy comprising: an object plane on which isdisposed a first surface of a substrate, wherein the substrate ischaracterized by a homogeneous refractive index (n_(sub)) and a surfacenormal; a first optical system disposed to provide a substantiallycoherent illumination of the object plane, the illuminationcharacterized by a wavelength λ and a radius of curvature and disposedat one of a plurality of incident wave vectors from about 0 to about2π/λ with respect to a surface normal of the substrate and at aplurality of azimuth angles spanning 0 to 2π; a second optical systemdisposed to collect portions of the illumination scattered from theobject plane, the second optical system having an optical axis disposedat one of a plurality of center wave vectors from about 0 to about 2π/λwith respect to the substrate surface normal and at the azimuth anglecorresponding to the illumination of the first optical system, whereinthe second optical system is characterized by a numerical aperture (NA);a third optical system disposed between the optical path of the firstoptical system and an entrance aperture of the first optical element ofthe second optical system to provide interferometric reintroduction of aportion of the coherent illumination (reference beam) into the secondoptical system, wherein each of an amplitude, a phase, a radius ofcurvature, and an angle of incidence of the reference beam is adjustedsuch that a corrected reference beam is present at the image plane ofthe second optical system; an electronic image device disposed at animage plane of the second optical system that responds linearly to thelocal optical intensity and transfers the local optical intensity mapacross the image plane (a sub-image) to a signal processor device inelectronic form; a device for adjusting the first, the second, and thethird optical systems to collect sub-images for different pairs of thepluralities of incident (first optical system) and collection center(second optical system) wave vectors so as to sequentially obtain aplurality of sub-images corresponding to a plurality of regions ofspatial frequency space; and an electronic device to sequentiallyreceive the electronic form of the sub-images and manipulate thesub-images to correct for distortions and alterations introduced by theoptical configuration, store, and combine the plurality of sub-imagescorresponding to the plurality of regions of spatial frequency space tocreate a composite image.
 2. The apparatus of claim 1, wherein the thirdoptical system further comprises: a first beamsplitter disposed in theoptical path of the first optical system to collect a portion of thecoherent illumination; one or more transfer optics disposed between thefirst optical system and the second optical system; and a secondbeamsplitter disposed between the object plane and a front aperture of acollection lens (objective) of the second optical system to reintroducethe portion of the coherent illumination as a reference beam into thesecond optical system at an angle θ less than the entrance angularaperture (<˜sin⁻¹ NA) of the second optical system.
 3. The apparatus ofclaim 1, wherein the third optical system further comprises: a firstbeamsplitter disposed in the optical path of the first optical system tocollect a portion of the coherent illumination; one or more transferoptics disposed between the first optical system and the second opticalsystem; and at least one of a grating or a grating on a waveguidedisposed between the object plane and a front aperture of the collectionlens (objective) of the second optical system to reintroduce the portionof the coherent illumination as a reference beam into the second opticalsystem at an angle θ less than the entrance angular aperture (<˜sin⁻¹NA) of the second optical system.
 4. The apparatus of claim 1, whereinthe third optical system further comprises: a first beamsplitterdisposed in the optical path of the first optical system to collect aportion of the coherent illumination; one or more optical components todirect the portion of the coherent illumination as a reference beam toilluminate the object at an angle θ corresponding to less than theentrance angular aperture (<˜sin⁻¹ NA) of the second optical system; anda dynamic (adjustable on/off) physical block disposed in a back pupilplane of the second optical system to alternately block and unblock asmall portion of the pupil aperture corresponding to the position of thereference beam in the aperture.
 5. The apparatus of claim 1, wherein thethird optical system further comprises: a first beamsplitter disposed inthe optical path of the first optical system to collect a portion of thecoherent plane wave illumination; and one or more optical components todirect the portion of the coherent illumination as a reference beam toilluminate the object plane at an angle θcorresponding to less than theentrance angular aperture (<˜sin⁻¹ NA) of the second collection opticalsystem; a guided-mode resonance filter (k-vector filter) disposedbetween the object plane and a collection lens of the second opticalsystem; and an another device to adjust the position, tilt, and rotationof the guided-mode resonance filter between positions, tilts, androtations in which it alternately transmits and blocks the portion ofthe reference beam transmitted through the object plane.
 6. Theapparatus of claim 1, wherein the first, the second, and the thirdoptical systems are arranged in at least one of a transmissionconfiguration and a reflection configuration.
 7. A method for microscopycomprising: providing an object disposed over a planar substrate,wherein the substrate is characterized by a homogeneous refractive index(n_(sub)) and a surface normal; providing a first optical system toilluminate the object with substantially coherent illumination, theillumination characterized by a wavelength λ and a radius of curvatureand disposed at one of a plurality of incident wave vectors from about 0to about 2π/λ with respect to a surface normal of the substrate and at aplurality of azimuth angles spanning from about 0 to about 2π; providinga second optical system disposed to collect portions of the illuminationscattered from the object plane, the second optical system having anoptical axis disposed at one of a plurality of center wave vectors fromabout 0 to about 2π/λ with respect to the substrate surface normal andat the azimuth angle corresponding to the illumination of the firstoptical system, wherein the second optical system is characterized by anumerical aperture (NA); providing a third optical system disposedbetween the optical path of the first optical system and an entranceaperture of the first optical element of the second optical system toprovide interferometric reintroduction of a portion of the coherentillumination (reference beam) into the second optical system, whereineach of an amplitude, a phase, a radius of curvature and an angle ofincidence of the reference is adjusted as required such that a correctedreference wave is present at the image plane of the second opticalsystem; recording a sub-image of the object at an object plane using anelectronic image device, wherein the sub-image is formed as a result ofinterference between the scattering resulting from the coherentillumination of the object and the reference beam; adjusting the first,the second, and the third optical systems to sequentially collect aplurality of sub-images corresponding to a plurality of regions ofspatial frequency space; manipulating each of the plurality ofsub-images using a signal processor to correct for distortions andalterations introduced by the optical configuration; and combining theplurality of sub-images into a composite image to provide asubstantially faithful image of the object.
 8. The method formicroscopy, according to claim 7, wherein the step of providing a thirdoptical system further comprises: collecting a portion of the coherentillumination using a beam splitter disposed in the optical path of thefirst optical system; providing one or more transfer optics; andreintroducing the portion of the coherent illumination as a referencebeam into the second optical system at an angle θ less than the entranceangular aperture (<˜sin⁻¹ NA) of the second optical system using asecond beamsplitter disposed between the object plane and a collectionlens of the second optical system.
 9. The method of microscopy,according to claim 8, wherein the angle 9 is adjusted to be close to,but less than, about sin⁻¹ (NA).
 10. The method for microscopy,according to claim 7, wherein the step of providing a third opticalsystem comprises: collecting a portion of the coherent illuminationusing a beam splitter disposed in the optical path of the first opticalsystem; providing one or more transfer optics; and reintroducing theportion of the coherent illumination as a reference beam into the secondoptical system at an angle θ less than the entrance angular aperture(<˜sin⁻¹ NA) of the second optical system using at least one of agrating or a grating on a waveguide disposed between the object planeand a collection lens of the second optical system.
 11. The method ofmicroscopy, according to claim 10, wherein the angle θ is adjusted to beclose to, but less than, sin⁻¹ (NA).
 12. The method for microscopy,according to claim 7, wherein the step of providing a third opticalsystem comprises: collecting a portion of the coherent illuminationusing a beam splitter disposed in the optical path of the first opticalsystem; directing the portion of the coherent illumination as areference beam to illuminate the object at an angle θ corresponding toless than the entrance angular aperture (<˜sin⁻¹ NA) of the secondoptical system using one or more optical components; and alternatelyblocking and unblocking a small portion of a back pupil aperture of thesecond optical system corresponding to the position of the referencebeam in the aperture using a dynamic (alternately on/off) physical blockdisposed in a back pupil plane of the second optical system.
 13. Themethod of claim 12 wherein the angle θ is chosen to be close to, butless than, sin⁻¹ (NA).
 14. The method for microscopy, according to claim7, wherein the step of providing a third optical system comprises:collecting a portion of the coherent illumination by splitting thecoherent illumination using a beam splitter disposed in the optical pathof the first optical system; directing the portion of the coherentillumination as a reference beam to illuminate the object at an angle θcorresponding to less than the entrance angular aperture (<˜sin⁻¹ NA) ofthe second optical system using one or more optical components betweenthe first optical system and the second optical system; and alternatelyblocking and unblocking the transmission of the reference beam byadjusting the position, tilt and rotation of a guide-mode resonancefilter (k-vector filter) disposed between the object and a collectionlens of the second optical system.
 15. The method of claim 12 whereinthe angle θ is chosen to be close to, but less than, sin⁻¹ (NA).
 16. Themethod for microscopy, according to claim 7, wherein the steps ofproviding the first, the second, and the third optical systems comprisesproviding the first, the second, and the third optical systems in atleast one of a transmission configuration and a reflectionconfiguration.
 17. The method for microscopy, according to claim 7further comprising one or more processes of subtraction of dark fieldimages, subtraction of background images, shifting of spatialfrequencies in accordance with the optical configuration, andelimination of one or more overlapping coverages of the frequency spacewherein the elimination operations can be performed either in theoptical systems or in the signal processing.
 18. The method formicroscopy, according to claim 7, further comprising selection of theregions of spatial frequency space to provide a more or less faithfulimage of the object in the object plane.
 19. An apparatus for microscopycomprising: an object plane on which is disposed a first surface of asubstrate, wherein the substrate is characterized by a homogeneousrefractive index (n_(sub)) and a surface normal; a first optical systemdisposed to provide an evanescent wave illumination of the object planeby providing a substantially coherent illumination of the object plane,the illumination characterized by a wavelength λ and a radius ofcurvature and disposed at one of a plurality of incident wave vectorsfrom about 2π/λ to about 2πn_(sub)/λ with respect to a surface normal ofthe substrate and at a multiplicity of azimuth angles spanning 0 to 2π,wherein the plurality of incident wave vectors correspond to anglesbeyond a total internal reflection angle θ_(c) of the substrate; asecond optical system disposed to collect portions of the illuminationscattered from the object plane, the second optical system having anoptical axis disposed at one of a plurality of center wave vectors fromabout 0 to about 2π/λ with respect to the substrate surface normal andat the azimuth angle corresponding to the illumination of the firstoptical system, wherein the second optical system is characterized by anumerical aperture (NA); a third optical system disposed in an opticalpath of the first optical system to provide interferometricreintroduction of a portion of the coherent illumination (referencebeam) into the second optical system, wherein each of an amplitude, aphase, a radius of curvature and an angle of incidence of the referenceis adjusted as required such that a corrected reference wave is presentat the image plane of the second optical system; an electronic imagedevice disposed at an image plane of the second optical system thatresponds linearly to the local optical intensity and transfers the localoptical intensity map across the image plane (a sub-image) to a signalprocessor device in electronic form; a device for adjusting the first,the second, and the third optical systems to collect sub-images fordifferent pairs of the pluralities of incident (first optical system)and collection center (second optical system) wave vectors so as tosequentially obtain a plurality of sub-images corresponding to aplurality of regions of spatial frequency space; and an electronicdevice to sequentially receive the electronic form of the sub-images andmanipulate the sub-images to correct for distortions and alterationsintroduced by the optical configuration, store, and combine theplurality of sub-images corresponding to the plurality of regions ofspatial frequency space to create a composite image.
 20. The apparatusof claim 19, wherein the third optical system further comprises: a firstbeamsplitter disposed in the optical path of the first optical systembefore the object to collect a portion of the coherent illumination; andone or more optics disposed between the first optical system and thesecond optical system to interferometrically reintroduce the portion ofthe coherent illumination as a reference beam into the second opticalsystem in a position after the exit aperture of a collection (objective)lens, wherein the reintroduction is at one of a position correspondingto a position a zero-order beam would have had if it had beentransmitted through a higher NA lens of the second optical system or analiased position to reduce pixel requirements of the electronic imagedevice, wherein the signal processor is adjusted to compensate for thisspatial frequency aliasing.
 21. The apparatus of claim 19, wherein thethird optical system further comprises: a first beamsplitter disposed inthe optical path of the first optical system to collect a portion of thecoherent illumination; one or more transfer optics disposed between thefirst optical system and the second optical system; and a secondbeamsplitter disposed between the object plane and the collection lensof the second optical system to reintroduce the portion of the coherentillumination as a reference beam into the second optical system at anangle θ less than the entrance angular aperture (<˜sin⁻¹ NA) of thesecond optical system.
 22. The apparatus of claim 19, wherein the thirdoptical system further comprises: a first beamsplitter disposed in theoptical path of the first optical system to collect a portion of thecoherent plane wave illumination; one or more transfer optics disposedbetween the first optical system and the second optical system; and atleast one of a grating or a grating on a waveguide disposed between theobject and a collection lens of the second optical system to reintroducethe portion of the coherent illumination as a reference beam into thesecond optical system at an angle θ less than the entrance angularaperture (<˜sin⁻¹ NA) of the second optical system.
 23. The apparatus ofclaim 19, wherein the third optical system further comprises: a firstbeamsplitter disposed in the optical path of the first optical system tocollect a portion of the coherent plane wave illumination; and one ormore optical components disposed between the first optical system andthe second optical system to direct the portion of the coherentillumination as a reference beam to illuminate the object at an angleθcorresponding to less than the entrance angular aperture (<˜sin⁻¹ NA)of the second optical system; and a dynamic (on/off) physical blockdisposed in a back pupil plane of the second optical system toalternately block and unblock a small portion of a pupil aperture,wherein the portion corresponds to the position of the reference beam inthe aperture.
 24. The apparatus of claim 19, wherein the third opticalsystem further comprises: a first beamsplitter disposed in the opticalpath of the first optical system to collect a portion of the coherentplane wave illumination; and one or more optical components disposedbetween the first optical system and the second optical system to directthe portion of the coherent illumination as a reference beam toilluminate the object at an angle θcorresponding to less than theentrance angular aperture (<˜sin⁻¹ NA) of said second collection opticalsystem; and an another device to adjust the position, tilt and rotationof the guided-mode resonance filter between positions, tilts androtations in which it sequentially transmits and blocks the portion ofthe reference beam transmitted through the object plane.
 25. A methodfor microscopy comprising: providing an object disposed over a surfaceof a planar substrate characterized by a homogeneous refractive index(n_(sub)) and a surface normal; providing a first optical systemdisposed to provide an evanescent wave illumination of the object planeby providing a substantially coherent illumination of the object plane,the illumination characterized by a wavelength λ and a radius ofcurvature and disposed at one of a plurality of incident wave vectorsfrom about λ to about 2πn_(sub)/λ with respect to a surface normal ofthe substrate and at a multiplicity of azimuth angles spanning 0 to 2π,wherein the plurality of incident wave vectors correspond to anglesbeyond a total internal reflection angle θ_(c) of the substrate;providing a second optical system having an optical axis disposed at oneof a plurality of center wave vectors from about 0 to about 2π/λ withrespect to the surface normal, wherein the second optical system ischaracterized by a numerical aperture (NA); providing a third opticalsystem disposed in an optical path of the first optical system toprovide interferometric reintroduction of a portion of the coherentplane wave illumination (reference beam) into the second optical system,wherein the amplitude, phase, and position of the reintroducedillumination plane wave in the back focal plane of the second opticalsystem is adjusted as required; recording a sub-image of the object atan object plane using an electronic image device, wherein the sub-imageis formed as a result of interference of the coherent plane waveillumination of the object and the reference beam; adjusting the first,the second, and the third optical systems to sequentially collect aplurality of sub-images corresponding to a plurality of regions ofspatial frequency space; manipulating each of the plurality ofsub-images using a signal processor to correct for distortions andalterations introduced by the optical configuration; and combining theplurality of sub-images into a composite image to provide asubstantially faithful image of the object.
 26. The method formicroscopy, according to claim 25, wherein the step of providing a thirdoptical system further comprises: collecting a portion of the coherentillumination by splitting the coherent illumination using a beamsplitter disposed in the optical path of the first optical system; andinterferometrically reintroducing the portion of the coherentillumination as a reference beam after the exit aperture of thecollection lens of the second optical system, wherein the reintroductionis at one of a position, an amplitude, a phase, a radius of curvatureand a angle of incidence onto the image plane either that a zero-orderbeam would have had if it had been transmitted through a higher NA lensof the second optical system or an aliased angle of incidence to reducepixel requirements of the electronic image device, wherein the signalprocessor is adjusted to compensate for this spatial frequency aliasing.27. The method for microscopy, according to claim 25, wherein the stepof providing a third optical system further comprises: collecting aportion of the coherent illumination by splitting the coherentillumination using a beam splitter disposed in the optical path of thefirst optical system; providing one or more transfer optics; andreintroducing the portion of the coherent illumination as a referencebeam into the second optical system at an angle θ less than the entranceangular aperture (<˜sin⁻¹ NA) of the second optical system using asecond beamsplitter disposed between the object and the entranceaperture of the collection lens of the second optical system, whereinthe reintroduction is at one of a position, an amplitude, a phase, aradius of curvature and an aliased angle of incidence onto the imageplane, wherein the signal processor is adjusted to compensate for thisspatial frequency aliasing.
 28. The method for microscopy, according toclaim 25, wherein the step of providing a third optical systemcomprises: collecting a portion of the coherent illumination using abeam splitter disposed in the optical path of the first optical system;providing one or more transfer optics; and reintroducing the portion ofthe coherent illumination as a reference beam into the second opticalsystem at an angle θ less than the entrance angular aperture (<˜sin⁻¹NA) of the second optical system using at least one of a grating or agrating on a waveguide disposed between the object and a collection lensof the second optical system.
 29. The method for microscopy, accordingto claim 25, wherein the step of providing a third optical systemcomprises: collecting a portion of the coherent plane wave illuminationby splitting the coherent plane wave illumination using a beam splitterdisposed in the optical path of the first optical system; directing theportion of the coherent plane wave illumination as a reference beam toilluminate the object at an angle θcorresponding to less than theentrance angular aperture (<˜sin⁻¹ NA) of the second optical systemusing one or more optical components disposed between the first opticalsystem and the second optical system; and alternately blocking andunblocking a small portion of the pupil aperture corresponding to theposition of the reference beam in the aperture using a dynamic (on/off)physical block disposed in a back pupil plane of the second opticalsystem.
 30. The method of claim 29 wherein the angle q is chosen to beclose to, but less than, sin⁻¹ (NA).
 31. The method for microscopy,according to claim 25, wherein the step of providing a third opticalsystem comprises: collecting a portion of the coherent plane waveillumination by splitting the coherent plane wave illumination using abeam splitter disposed in the optical path of the first optical system;directing the portion of the coherent plane wave illumination as areference beam to illuminate the object at an angle θ corresponding toless than the entrance angular aperture (<˜sin⁻¹ NA) of the secondoptical system using one or more optical components between the firstoptical system and the second optical system; and sequentially blockingand unblocking the transmission of the reference beam using a guide-moderesonance filter (k-vector filter) disposed between the object and acollection lens of the second optical system.
 32. The method of claim 31wherein the angle q is chosen to be close to, but less than, sin⁻¹(NA).33. The method for microscopy, according to claim 25 further comprisingone or more processes of subtraction of dark field images, subtractionof background images, shifting of spatial frequencies in accordance withthe optical configuration, and elimination of one or more overlappingcoverages of the frequency space wherein the elimination operations canbe performed either in the optical systems or in the signal processing.34. The method for microscopy, according to claim 25, further comprisingselection of the regions of spatial frequency space to provide a more orless faithful image of the object in the object plane.
 35. An apparatusfor microscopy comprising: an object plane on which is disposed a firstsurface of a planar substrate, wherein the substrate is characterized bya homogeneous refractive index (n_(sub)) and a surface normal; a firstoptical system disposed to provide a substantially coherent illuminationof the object plane, the illumination characterized by a wavelength Kand a radius of curvature and disposed at one of a plurality of incidentwave vectors from about 0 to about 2πn_(sub)/λ with respect to a surfacenormal of the substrate and at a plurality of azimuth angles spanning 0to 2π; at least one grating on the side of the substrate opposite theobject plane, each grating characterized by a period, a depth, a gratingprofile and a position to further scatter reflected waves resulting fromthe coherent illumination of the object plane into propagating waves inthe medium below the substrate; a second optical system having anoptical axis disposed at one of a plurality of center wave vectors fromabout 0 to about 2π/λ with respect to the surface normal, wherein thesecond optical system comprises the gratings on the second side of thesubstrate and is characterized by a numerical aperture (NA); a thirdoptical system disposed in an optical path of the first optical systemto provide interferometric reintroduction of a portion of the coherentillumination (reference beam) into the second optical system, whereineach of an amplitude, a phase, a radius of curvature and an angle ofincidence of the reference is adjusted as required such that a correctedreference wave is present at the image plane of the second opticalsystem; an electronic image device disposed at an image plane of thesecond optical system that responds linearly to the local opticalintensity and transfers the local optical intensity map across the imageplane (a sub-image) to a signal processor device in electronic form; adevice for adjusting the first, the second, and the third opticalsystems to collect sub-images for different pairs of the pluralities ofincident (first optical system) and collection center (second opticalsystem) wave vectors so as to sequentially obtain a plurality ofsub-images corresponding to a plurality of regions of spatial frequencyspace; and an electronic device to sequentially receive the electronicform of the sub-images and manipulate the sub-images to correct fordistortions and alterations introduced by the optical configuration,store, and combine the plurality of sub-images corresponding to theplurality of regions of spatial frequency space to create a compositeimage.
 36. The apparatus of claim 35, wherein the third optical systemfurther comprises: a first beamsplitter disposed in the optical path ofthe first optical system before the object to collect a portion of thecoherent plane wave illumination; and one or more optics disposedbetween the first optical system and the second optical system tointerferometrically reintroduce the portion of the coherent illuminationas a reference beam into the second optical system in a position afterthe exit aperture of a collection (objective) lens, wherein thereintroduction is at one of a position corresponding to a position azero-order beam would have had if it had been transmitted through ahigher NA lens of the second optical system or an aliased position toreduce pixel requirements of the electronic image device, wherein thesignal processor is adjusted to compensate for this spatial frequencyaliasing.
 37. The apparatus of claim 35, wherein the third opticalsystem further comprises: a first beamsplitter disposed in the opticalpath of the first optical system to collect a portion of the coherentplane wave illumination; one or more transfer optics disposed betweenthe first optical system and the second optical system; and a secondbeamsplitter disposed between the object and the collection lens of thesecond optical system to reintroduce the portion of the coherentillumination as a reference beam into the second optical system at anangle θ less than the entrance angular aperture (<˜sin⁻¹ NA) of thesecond optical system.
 38. The apparatus of claim 35, wherein the thirdoptical system further comprises: a first beamsplitter disposed in theoptical path of the first optical system to collect a portion of thecoherent plane wave illumination; one or more transfer optics disposedbetween the first optical system and the second optical system; and atleast one of a grating or a grating on a waveguide disposed between theobject and a collection lens of the second optical system to reintroducethe portion of the coherent plane wave illumination as a reference beaminto the second optical system at an angle θ less than the entranceangular aperture (<˜sin⁻¹ NA) of the second collection optical system.39. The apparatus of claim 35, wherein the third optical system furthercomprises: a first beamsplitter disposed in the optical path of thefirst optical system to collect a portion of the coherent plane waveillumination; and one or more optical components disposed between thefirst optical system and the second optical system to direct the portionof the coherent plane wave illumination as a reference beam toilluminate the object at an angle θ corresponding to less than theentrance angular aperture (<˜sin⁻¹ NA) of the second optical system; anda dynamic (on/off) physical block disposed in a back pupil plane of thesecond optical system to alternately block and unblock a small portionof the pupil aperture corresponding to the position of the referencebeam in the aperture.
 40. The apparatus of claim 35, wherein the thirdoptical system further comprises: a first beamsplitter disposed in theoptical path of the first optical system to collect a portion of thecoherent plane wave illumination; and one or more optical componentsdisposed between the first optical system and the second optical systemto direct the portion of the coherent plane wave illumination as areference beam to illuminate the object at an angle θ corresponding toless than the entrance angular aperture (<˜sin⁻¹ NA) of said secondcollection optical system; and a guided-mode resonance filter (k-vectorfilter) disposed between the object and a collection lens of the secondoptical system to sequentially block and unblock the transmission of thereference beam.
 41. A method for microscopy comprising: providing anobject disposed over a first side of a planar substrate, the substratecharacterized by a homogeneous refractive index (n_(sub)) and a surfacenormal such that the object is separated from the substrate by adistance of no more than about ≦λ; providing at least one grating on asecond side of the substrate opposite the first side, each gratingcharacterized by a position, a period, a depth, and a grating profile,wherein the at least grating further scatters reflected waves resultingfrom the coherent illumination of the object into propagating waves inthe medium below the substrate; providing a first optical systemdisposed to provide a substantially coherent illumination of the objectplane, the illumination characterized by a wavelength λ and a radius ofcurvature and disposed at one of a plurality of incident wavevectorsfrom about 0 to about 2πn_(sub)/λ with respect to a surface normal ofthe substrate and at a plurality of azimuth angles spanning about 0 toabout 2π; providing a second optical system having an optical axisdisposed at one of a plurality of center wave vectors from about 0 toabout 2π/λ with respect to the surface normal, wherein the secondoptical system comprises the at least one grating on the second side ofthe substrate and is characterized by a numerical aperture (NA);providing a third optical system disposed in an optical path of thefirst optical system to provide interferometric reintroduction of aportion of the coherent illumination (reference beam) into the secondoptical system, wherein each of an amplitude, a phase, a radius ofcurvature and an angle of incidence of the reference is adjusted asrequired such that a corrected reference wave is present at the imageplane of the second optical system; recording a sub-image of the objectat an object plane using an electronic image device, wherein thesub-image is formed as a result of interference between the scatteringresulting from the coherent illumination of the object and the referencebeam; adjusting the first, the second, and the third optical systems tosequentially collect a plurality of sub-images corresponding to aplurality of regions of spatial frequency space; manipulating each ofthe plurality of sub-images using a signal processor to correct fordistortions and alterations introduced by the optical configuration; andcombining the plurality of sub-images into a composite image to providea substantially faithful image of the object.
 42. The method formicroscopy, according to claim 41, wherein the step of providing a thirdoptical system further comprises: collecting a portion of the coherentillumination by splitting the coherent illumination using a beamsplitter disposed in the optical path of the first optical system; andinterferometrically reintroducing the portion of the coherentillumination as a reference beam after the exit aperture of thecollection lens of the second optical system, wherein the reintroductionis at one of a position, an amplitude, a phase, a radius of curvatureand a angle of incidence onto the image plane that either a zero-orderbeam would have had if it had been transmitted through a higher NA lensof the second optical system or an aliased angle of incidence to reducepixel requirements of the electronic image device, wherein the signalprocessor is adjusted to compensate for this spatial frequency aliasing.43. The method for microscopy, according to claim 41, wherein the stepof providing a third optical system further comprises: collecting aportion of the coherent illumination using a beam splitter disposed inthe optical path of the first optical system; providing one or moretransfer optics; and reintroducing the portion of the coherentillumination as a reference beam into the second optical system at anangle θ less than the entrance angular aperture (<˜sin⁻¹ NA) of thesecond optical system using a second beamsplitter disposed between theobject and the collection lens of the second optical system.
 44. Themethod of claim 43 wherein the angle θ is chosen to be close to, butless than, sin⁻¹(NA).
 45. The method for microscopy, according to claim41, wherein the step of providing a third optical system comprises:collecting a portion of the coherent plane wave illumination using abeam splitter disposed in the optical path of the first optical system;providing one or more transfer optics; and reintroducing the portion ofthe coherent illumination as a reference beam into the second opticalsystem at an angle θ less than the entrance angular aperture (<˜sin⁻¹NA) of the second optical system using at least one of a grating or agrating on a waveguide disposed between the object and a collection lensof the second optical system.
 46. The method of claim 45 wherein theangle θ is chosen to be close to, but less than, sin⁻¹ (NA).
 47. Themethod for microscopy, according to claim 41, wherein the step ofproviding a third optical system comprises: collecting a portion of thecoherent illumination using a beam splitter disposed in the optical pathof the first optical system; directing the portion of the coherentillumination as a reference beam to illuminate the object at an angle θcorresponding to less than the entrance angular aperture (<˜sin⁻¹ NA) ofthe second optical system using one or more optical components disposedbetween the first optical system and the second optical system; andalternately blocking and unblocking a small portion of the pupilaperture corresponding to the position of the reference beam in theaperture using a dynamic (on/off) physical block disposed in a backpupil plane of the second optical system.
 48. The method of claim 47wherein the angle θ is chosen to be close to, but less than, sin⁻¹(NA).49. The method for microscopy, according to claim 41 further comprisingone or more processes of subtraction of dark field images, subtractionof background images, shifting of spatial frequencies in accordance withthe optical configuration, and elimination of one or more overlappingcoverages of the frequency space wherein the elimination operations canbe performed either in the optical systems or in the signal processing.50. The method for microscopy, according to claim 41, further comprisingselection of the regions of spatial frequency space to provide a more orless faithful image of the object in the object plane.
 51. An apparatusfor coherent anti-Stokes Raman (CARS) microscopy comprising: an objectplane on which is disposed a first surface of a planar substrate,wherein the substrate is characterized by a homogeneous refractive index(n_(sub)) and a surface normal; a first optical system disposed toprovide a illumination of the object plane, the illuminationcharacterized by two substantially coincident coherent beams withwavelengths λ₁ and λ₂ and corresponding angular frequencies ω₁ and ω₂with ω₁>ω₂, a radius of curvature, and disposed at one of a plurality ofincident wave vectors from about 0 to about 2πn_(sub)/λ₁ with respect toa surface normal of the substrate and at a plurality of azimuth anglesspanning about 0 to about 2π; a second optical system (collection)having an optical axis disposed at one of a plurality of center wavevectors from about 0 to about 2πn_(sub)/λ₁ with respect to the surfacenormal, wherein the second optical system is characterized by anumerical aperture (NA) and is responsive primarily to optical signalsat frequencies greater than ω₁; a third optical system disposed in anoptical path of the first optical system to provide interferometricreintroduction of a reference illumination (reference beam) at afrequency of 2ω₁−ω₂, into the second optical system, wherein each of anamplitude, a phase, a radius of curvature and an angle of incidence ofthe reference is adjusted as required such that a corrected referencewave is present at the image plane of the second optical system; anelectronic image device disposed at an image plane of the second opticalsystem that responds linearly to the local optical intensity andtransfers the local optical intensity map across the image plane (asub-image) to a signal processor device in electronic form; a device foradjusting the first, the second, and the third optical systems tocollect sub-images for different pairs of the pluralities of incident(first optical system) and collection center (second optical system)wave vectors so as to sequentially obtain a plurality of sub-imagescorresponding to a plurality of regions of spatial frequency space; andan electronic device to sequentially receive the electronic form of thesub-images and manipulate the sub-images to correct for distortions andalterations introduced by the optical configuration, store, and combinethe plurality of sub-images corresponding to the plurality of regions ofspatial frequency space to create a composite image.
 52. The apparatusof claim 51, wherein the substrate is air.
 53. The apparatus of claim51, wherein the third optical system further comprises: a firstbeamsplitter disposed in the optical path of the first optical systembefore the object to collect a portion of the coherent illumination; andone or more optics disposed between the first optical system and thesecond optical system, wherein the optics comprises a nonresonantnonlinear material configured to generate the anti-Stokes four-wavemixing frequency 2ω₁−ω₂ and exclude the fundamental frequencies (ω₁ andω₂), and to interferometrically reintroduce the portion of theanti-Stokes coherent illumination as a reference beam into the secondoptical system in a position after the exit aperture of a collection(objective) lens, wherein the reintroduction is at one of a positioncorresponding to a position a zero-order beam would have had if it hadbeen transmitted through an appropriate higher NA lens of the secondoptical system or an aliased position to reduce pixel requirements ofthe electronic image device, wherein the signal processor is adjusted tocompensate for this spatial frequency aliasing.
 54. The apparatus ofclaim 51, wherein the third optical system further comprises: a firstbeamsplitter disposed in the optical path of the first optical system tocollect a portion of the coherent plane wave illumination; one or moretransfer optics disposed between the first optical system and the secondoptical system, wherein the optics comprises a nonresonant nonlinearmaterial configured to generate the anti-Stokes four-wave mixingfrequency 2ω₁−ω₂ and exclude the fundamental frequencies (ω₁ and ω₂);and a second beamsplitter disposed between the object and the collectionlens of the second optical system to reintroduce the portion of theanti-Stokes coherent plane wave illumination as a reference beam intothe second optical system at an angle θ less than the entrance angularaperture (<˜sin⁻¹ NA) of the second optical system.
 55. The apparatus ofclaim 51, wherein the third optical system further comprises: a firstbeamsplitter disposed in the optical path of the first optical system tocollect a portion of the coherent plane wave illumination; one or moretransfer optics disposed between the first optical system and the secondoptical system, wherein the optics comprises a nonresonant nonlinearmaterial configured to generate the anti-Stokes four-wave mixingfrequency 2ω₁−ω₂ and exclude the fundamental frequencies (ω₁ and ω₂);and at least one of a grating or a grating on a waveguide disposedbetween the object and a collection lens of the second optical system toreintroduce the portion of the anti-Stokes coherent plane waveillumination as a reference beam into the second optical system at anangle α less than the entrance angular aperture (<˜sin⁻¹ NA) of thesecond collection optical system.
 56. The apparatus of claim 51, whereinthe third optical system further comprises: a first beamsplitterdisposed in the optical path of the first optical system to collect aportion of the coherent plane wave illumination; and one or moretransfer optics, wherein the optics comprises a nonresonant nonlinearmaterial configured to generate the anti-Stokes four-wave mixingfrequency 2ω₁−ω₂ and exclude the fundamental frequencies (ω₁ and ω₂);and means to direct the portion of the anti-Stokes coherent plane waveillumination as a reference beam to illuminate the object at an angle θcorresponding to less than the entrance angular aperture (<˜sin⁻¹ NA) ofthe second optical system; and a dynamic (on/off) physical blockdisposed in a back pupil plane of the second optical system toalternately block and unblock a small portion of the pupil aperturecorresponding to the position of the reference beam in the aperture. 57.The apparatus of claim 51, wherein the third optical system furthercomprises: a first beamsplitter disposed in the optical path of thefirst optical system to collect a portion of the coherent plane waveillumination; and one or more transfer optics, wherein the opticscomprises a nonresonant nonlinear material configured to generate theanti-Stokes four-wave mixing frequency 2ω₁−ω₂ and exclude thefundamental frequencies (ω₁ and ω₂); and means to direct the portion ofthe anti-Stokes coherent plane wave illumination as a reference beam toilluminate the object at an angle θ corresponding to less than theentrance angular aperture (<˜sin⁻¹ NA) of the second optical system; anda guided-mode resonance filter (k-vector filter) disposed between theobject and a collection lens of the second optical system tosequentially block and unblock the transmission of the reference beam.58. The apparatus of claim 51 further comprising at least one knownreference object to cover a small part of the image field.
 59. Theapparatus of claim 51, wherein the first, the second, and the thirdoptical systems are arranged in at least one of a transmissionconfiguration and a reflection configuration.
 60. The apparatus of claim53, wherein the plurality of incident wave vectors of the first opticalsystem comprises only wave vectors <2π/λ₁ wherein these wave vectors areaccessed by illumination of the substrate at polar angles between 0 andπ/2.
 61. The apparatus of claim 53, wherein the plurality of incidentwave vectors of the first optical system comprises wave vectors between2π/λ₁ and 2πn_(sub)/λ₁, wherein these wave vectors are accessed byevanescent wave illumination of the object through the substrate. 62.The apparatus of claim 53, wherein the plurality of center wave vectorsof the second optical system comprises only center wave vectors <2π/λ₁,wherein these center wave vectors are accessed by an optical systemabove the object plane of the substrate.
 63. The apparatus of claim 53,wherein the plurality of center wave vectors of the second opticalsystem comprises center wave vectors between 2π/λ₁ and 2πn_(sub)/λ₁,wherein the center wave vectors greater than 2π/λ₁ are accessed throughthe substrate and the second optical system comprises a plurality ofgratings on the side of the planar substrate opposite the object plane,wherein each grating is characterized by a position, a pitch, and agrating profile.
 64. A method for coherent anti-Stokes Raman (CARS)microscopy comprising: providing an object atop an object plane disposedupon a planar substrate, wherein the substrate is characterized by ahomogeneous refractive index (n_(sub)) and a surface normal; providing afirst optical system disposed to provide a illumination of the objectplane, the illumination characterized by two substantially coincidentcoherent beams with wavelengths λ₁ and λ₂ and corresponding angularfrequencies ω₁ and ω₂ with ω₁>ω₂, a radius of curvature, and disposed atone of a plurality of incident wave vectors from about 0 to about2πn_(sub)/λ₁ with respect to a surface normal of the substrate and at aplurality of azimuth angles spanning 0 to 2π; providing a second opticalsystem (collection) having an optical axis disposed at one of aplurality of center wave vectors from about 0 to about 2πnsub/λ₁ withrespect to the surface normal, wherein the second optical system ischaracterized by a numerical aperture (NA) and is responsive primarilyto optical signals at frequencies greater than ω₁; providing a thirdoptical system disposed in an optical path of the first optical systemto provide interferometric reintroduction of a reference illumination(reference beam) at a frequency of 2ω₁−ω₂, into the second opticalsystem, wherein each of an amplitude, a phase, a radius of curvature andan angle of incidence of the reference is adjusted as required such thata corrected reference wave is present at the image plane of the secondoptical system; recording a sub-image of the object at an object planeusing an electronic image device, wherein the sub-image is formed as aresult of interference between the scattering resulting from thecoherent illumination of the object and the reference beam; adjustingthe first, the second, and the third optical systems to sequentiallycollect a plurality of sub-images corresponding to a plurality ofregions of spatial frequency space; manipulating each of the pluralityof sub-images using a signal processor to correct for distortions andalterations introduced by the optical configuration; and combining theplurality of sub-images into a composite image to provide asubstantially faithful image of the object.
 65. The method for coherentanti-Stokes Raman (CARS) microscopy, according to claim 64, furthercomprising tuning a frequency difference ω₁−ω₂ of the two substantiallycoplanar and spatially coherent plane waves through Raman resonances ofone or more materials in the object.
 66. The method for coherentanti-Stokes Raman (CARS) microscopy, according to claim 64, wherein thesubstrate is air.
 67. The method for coherent anti-Stokes Raman (CARS)microscopy, according to claim 64, wherein the step of providing a thirdoptical system further comprises: collecting a portion of the coherentillumination using a first beamsplitter disposed in the optical path ofthe first optical system; and interferometrically reintroducing one ormore optics disposed between the first optical system and the secondoptical system, a coherent anti-Stokes (2ω₁−ω₂) reference beam, andexcluding the fundamental frequencies (ω₁ and ω₂), into the secondoptical system in a position after the exit aperture of a collection(objective) lens, wherein the reintroduction is at one of a positioncorresponding to a position a zero-order beam would have had if it hadbeen transmitted through an appropriate higher NA lens of the secondoptical system or an aliased position to reduce pixel requirements ofthe electronic image device, wherein the signal processor is adjusted tocompensate for this spatial frequency aliasing.
 68. The method forcoherent anti-Stokes Raman (CARS) microscopy, according to claim 64,wherein the step of providing a third optical system further comprises:providing a first beamsplitter in the optical path of the first opticalsystem to collect a portion of the coherent plane wave illumination;using one or more transfer optics disposed between the first opticalsystem and the second optical system, wherein the optics comprises anonresonant nonlinear material configured to generate the anti-Stokesfour-wave mixing frequency 2ω₁−ω₂ and exclude the fundamentalfrequencies (ω₁ and ω₂); and interferometrically injecting ananti-Stokes reference beam using a second beamsplitter disposed betweenthe object and the collection lens of the second optical system at anangle θ less than the entrance angular aperture (<˜sin⁻¹ NA) of thesecond optical system.
 69. The method for coherent anti-Stokes Raman(CARS) microscopy, according to claim 51, wherein the step of providingthe third optical system further comprises: providing a firstbeamsplitter in the optical path of the first optical system to collecta portion of the coherent plane wave illumination; providing one or moretransfer optics disposed between the first optical system and the secondoptical system, wherein the optics comprises a nonresonant nonlinearmaterial configured to generate the anti-Stokes four-wave mixingfrequency 2ω₁−ω₂ and exclude the fundamental frequencies (ω₁ and ω₂);and using at least one of a grating or a grating on a waveguide disposedbetween the object and a collection lens of the second optical system toreintroduce the portion of the anti-Stokes coherent plane waveillumination as a reference beam into the second optical system at anangle θless than the entrance angular aperture (<˜sin⁻¹ NA) of thesecond collection optical system.
 70. The method for coherentanti-Stokes Raman (CARS) microscopy, according to claim 64, wherein thestep of providing the third optical system further comprises: providinga first beamsplitter in the optical path of the first optical system tocollect a portion of the coherent plane wave illumination; and using oneor more transfer optics, wherein the optics comprises a nonresonantnonlinear material configured to generate the anti-Stokes four-wavemixing frequency 2ω₁−ω₂ and exclude the fundamental frequencies (ω₁ andω₂), to direct the portion of the anti-Stokes coherent plane waveillumination as a reference beam to illuminate the object at an angle θcorresponding to less than the entrance angular aperture (<˜sin⁻¹ NA) ofthe second optical system; and providing a dynamic (on/off) physicalblock disposed in a back pupil plane of the second optical system toalternately block and unblock a small portion of the pupil aperturecorresponding to the position of the reference beam in the aperture. 71.The method for coherent anti-Stokes Raman (CARS) microscopy, accordingto claim 64, wherein the step of providing the third optical systemfurther comprises: providing a first beamsplitter in the optical path ofthe first optical system to collect a portion of the coherent plane waveillumination; providing one or more transfer optics, wherein the opticscomprises a nonresonant nonlinear material configured to generate theanti-Stokes four-wave mixing frequency 2ω₁−ω₂ and exclude thefundamental frequencies (ω₁ and ω₂); and means to direct the portion ofthe anti-Stokes coherent plane wave illumination as a reference beam toilluminate the object at an angle θ corresponding to less than theentrance angular aperture (>˜sin⁻¹ NA) of the second optical system; andproviding a guided-mode resonance filter (k-vector filter) between theobject and a collection lens of the second optical system tosequentially block and unblock the transmission of the reference beam.72. The method for coherent anti-Stokes Raman (CARS) microscopy,according to claim 64 further comprising providing at least one knownreference object to cover a small part of the image field.
 73. Themethod for coherent anti-Stokes Raman (CARS) microscopy, according toclaim 64, wherein the first, the second, and the third optical systemsare arranged in at least one of a transmission configuration and areflection configuration.
 74. The method of claim 64, wherein theplurality of incident wave vectors of the first optical system comprisesonly wave vectors <2π/λ₁ wherein these wave vectors are accessed byillumination of the substrate at polar angles between 0 and π/2.
 75. Themethod for coherent anti-Stokes Raman (CARS) microscopy, according toclaim 64, wherein the plurality of incident wave vectors of the firstoptical system comprises wave vectors between 2π/λ₁ and 2πn_(sub)/λ₁,wherein these wave vectors are accessed by evanescent wave illuminationof the object through the substrate.
 76. The method for coherentanti-Stokes Raman (CARS) microscopy, according to claim 64, wherein theplurality of center wave vectors of the second optical system comprisesonly center wave vectors<2π/λ₁, wherein these center wave vectors areaccessed by an optical system above the object plane of the substrate.77. The method for coherent anti-Stokes Raman (CARS) microscopy,according to, according to claim 64, wherein the plurality of centerwave vectors of the second optical system comprises center wave vectorsbetween 2π/λ₁ and 2πn_(sub)/λ₁, wherein the center wave vectors greaterthan 2π/λ₁ are accessed through the substrate and the second opticalsystem comprises a plurality of gratings on the side of the planarsubstrate opposite the object plane, wherein each grating ischaracterized by a position, a pitch, and a grating profile.
 78. Themethod for coherent anti-Stokes Raman (CARS) microscopy, according tomicroscopy, according to claim 64 further comprising one or moreprocesses of subtraction of dark field images, subtraction of backgroundimages, shifting of spatial frequencies in accordance with the opticalconfiguration, and elimination of one or more overlapping coverages ofthe frequency space wherein the elimination operations can be performedeither in the optical systems or in the signal processing.
 79. Themethod for coherent anti-Stokes Raman (CARS) microscopy, according toclaim 64, further comprising selection of the regions of spatialfrequency space to provide a more or less faithful image of the objectin the object plane.